Recent zbMATH articles in MSC 70https://www.zbmath.org/atom/cc/702022-05-16T20:40:13.078697ZUnknown authorWerkzeugMathematical analysis in interdisciplinary researchhttps://www.zbmath.org/1483.000422022-05-16T20:40:13.078697ZPublisher's description: This contributed volume provides an extensive account of research and expository papers in a broad domain of mathematical analysis and its various applications to a multitude of fields. Presenting the state-of-the-art knowledge in a wide range of topics, the book will be useful to graduate students and researchers in theoretical and applicable interdisciplinary research. The focus is on several subjects including: optimal control problems, optimal maintenance of communication networks, optimal emergency evacuation with uncertainty, cooperative and noncooperative partial differential systems, variational inequalities and general equilibrium models, anisotropic elasticity and harmonic functions, nonlinear stochastic differential equations, operator equations, max-product operators of Kantorovich type, perturbations of operators, integral operators, dynamical systems involving maximal monotone operators, the three-body problem, deceptive systems, hyperbolic equations, strongly generalized preinvex functions, Dirichlet characters, probability distribution functions, applied statistics, integral inequalities, generalized convexity, global hyperbolicity of spacetimes, Douglas-Rachford methods, fixed point problems, the general Rodrigues problem, Banach algebras, affine group, Gibbs semigroup, relator spaces, sparse data representation, Meier-Keeler sequential contractions, hybrid contractions, and polynomial equations. Some of the works published within this volume provide as well guidelines for further research and proposals for new directions and open problems.
The articles of mathematical interest will be reviewed individually.Barak-Erdős graphs and the infinite-bin modelhttps://www.zbmath.org/1483.051622022-05-16T20:40:13.078697Z"Mallein, Bastien"https://www.zbmath.org/authors/?q=ai:mallein.bastien"Ramassamy, Sanjay"https://www.zbmath.org/authors/?q=ai:ramassamy.sanjaySummary: A Barak-Erdős graph is a directed acyclic version of the Erdős-Rényi random graph. It is obtained by performing independent bond percolation with parameter \(p\) on the complete graph with vertices \(\{1,\dots,n\}\), in which the edge between two vertices \(i< j\) is directed from \(i\) to \(j\). The length of the longest path in this graph grows linearly with the number of vertices, at rate \(C(p)\). In this article, we use a coupling between Barak-Erdős graphs and infinite-bin models to provide explicit estimates on \(C(p)\). More precisely, we prove that the front of an infinite-bin model grows at linear speed, and that this speed can be obtained as the sum of a series. Using these results, we prove the analyticity of \(C\) for \(p> 1/2\), and compute its power series expansion. We also obtain the first two terms of the asymptotic expansion of \(C\) as \(p\to 0\), using a coupling with branching random walks with selection.The Riemann-Hilbert problem in irregular cases (after works by D'Agnolo, Kashiwara, Mochizuki and Schapira)https://www.zbmath.org/1483.140342022-05-16T20:40:13.078697Z"Guillermou, Stéphane"https://www.zbmath.org/authors/?q=ai:guillermou.stephaneSummary: With a \(\mathcal D\)-module \(\mathcal M\) (roughly speaking, a system of linear PDE's with holomorphic coefficients) on a complex manifold \(X\), we associate its sheaf of holomorphic solutions, \(\mathcal Sol(\mathcal M)\). If \(\mathcal M\) is holonomic (it contains ``many'' equations) then \(\mathcal Sol(\mathcal M)\) has finiteness properties. If, moreover, \(\mathcal M\) has regular singularities, it is known from the 80's that \(\mathcal Sol(\mathcal M)\) determines \(\mathcal M\). Recent works of D'Agnolo, Kashiwara, Mochizuki, Schapira allow us to treat the general holonomic case.
For the entire collection see [Zbl 1416.00029].Backbone curves of coupled cubic oscillators in one-to-one internal resonance: bifurcation scenario, measurements and parameter identificationhttps://www.zbmath.org/1483.340502022-05-16T20:40:13.078697Z"Givois, Arthur"https://www.zbmath.org/authors/?q=ai:givois.arthur"Tan, Jin-Jack"https://www.zbmath.org/authors/?q=ai:tan.jin-jack"Touzé, Cyril"https://www.zbmath.org/authors/?q=ai:touze.cyril"Thomas, Olivier"https://www.zbmath.org/authors/?q=ai:thomas.olivierSummary: A system composed of two cubic nonlinear oscillators with close natural frequencies, and thus displaying a 1:1 internal resonance, is studied both theoretically and experimentally, with a special emphasis on the free oscillations and the backbone curves. The instability regions of uncoupled solutions are derived and the bifurcation scenario as a function of the parameters of the problem is established, showing in an exhaustive manner all possible solutions. The backbone curves are then experimentally measured on a circular plate, where the asymmetric modes are known to display companion configurations with close eigenfrequencies. A control system based on a Phase-Locked Loop (PLL) is used to measure the backbone curves and also the frequency response function in the forced and damped case, including unstable branches. The model is used for a complete identification of the unknown parameters and an excellent comparison is drawn out between theoretical prediction and measurements.Dynamics of non-autonomous oscillator with a controlled phase and frequency of external forcinghttps://www.zbmath.org/1483.340522022-05-16T20:40:13.078697Z"Krylosova, D. A."https://www.zbmath.org/authors/?q=ai:krylosova.d-a"Seleznev, E. P."https://www.zbmath.org/authors/?q=ai:seleznev.eugene-p"Stankevich, N. V."https://www.zbmath.org/authors/?q=ai:stankevich.nataliya-vladimirovnaSummary: The dynamics of a non-autonomous oscillator in which the phase and frequency of the external force depend on the dynamical variable is studied. Such a control of the phase and frequency of the external force leads to the appearance of complex chaotic dynamics in the behavior of oscillator. A hierarchy of various periodic and chaotic oscillations is observed. The structure of the space of control parameters is studied. It is shown there are oscillatory modes similar to those of a non-autonomous oscillator with a potential in the form of a periodic function in the system dynamics, but there are also significant differences. Physical experiments of such systems are implemented.Composite synchronization of four exciters driven by induction motors in a vibration systemhttps://www.zbmath.org/1483.340742022-05-16T20:40:13.078697Z"Kong, Xiangxi"https://www.zbmath.org/authors/?q=ai:kong.xiangxi"Zhou, Chong"https://www.zbmath.org/authors/?q=ai:zhou.chong"Wen, Bangchun"https://www.zbmath.org/authors/?q=ai:wen.bangchunSummary: In this paper, a newly composite synchronization scheme is proposed to ensure the straight line vibration form of a linear vibration system driven by four exciters. Composite synchronization is a combination of self-synchronization and controlled synchronization. Firstly, controlled synchronization of two pairs of homodromous coupling exciters with zero phase differences is implemented by using the master-slave control structure and the adaptive sliding mode control algorithm. On basis of controlled synchronization, self-synchronization of two coupling exciters rotating in the opposite directions is studied. Based on the perturbation method, the synchronization and stability conditions of composite synchronization are obtained. The theoretical results indicate that composite synchronization of four exciters with zero phase differences can be implemented with different supply frequencies and the straight line vibration form of the linear vibration system also can be obtained. Some simulations are conducted to verify the feasibility of the proposed composite synchronization scheme. The effects of some structural parameters on composite synchronization of four exciters are discussed. Finally, some experiments are operated to validate the effectiveness of the proposed composite synchronization scheme.Recurrent solutions of the Korteweg-de Vries equation with boundary forcehttps://www.zbmath.org/1483.351832022-05-16T20:40:13.078697Z"Chen, Mo"https://www.zbmath.org/authors/?q=ai:chen.moSummary: In this paper, we will establish the existence of the bounded solution, periodic solution, quasi-periodic solution and almost periodic solution for the Korteweg-de Vries equation with boundary force.Scaling laws in dynamical systemshttps://www.zbmath.org/1483.370022022-05-16T20:40:13.078697Z"Leonel, Edson Denis"https://www.zbmath.org/authors/?q=ai:leonel.edson-denisThe author presents and combines various approaches and results on nonlinear dynamical systems with special emphasis on the scaling formalism.
The titles of the chapters are quite informative and they reflect not only the structure of the book but also its content:
1. Introduction, 2. One-Dimensional Mappings, 3. Some Dynamical Properties for the Logistic Map, 4. The Logistic-Like Map, 5. Introduction to Two Dimensional Mappings, 6. A Fermi Accelerator Model; 7. Dissipation in the Fermi-Ulam Model; 8. Dynamical Properties for a Bouncer Model; 9. Localization of Invariant Spanning Curves; 10. Chaotic Diffusion in Non-Dissipative Mappings; 11. Scaling on a Dissipative Standard Mapping; 12. Introduction to Billiard Dynamics; 13. Time Dependent Billiards; 14. Suppression of Fermi Acceleration in the Oval Billiard; 15. A Thermodynamic Model for Time Dependent Billiards.
The book provides useful introductory materials, including exercises, for undergraduate and graduate students who wish to have an overview of common scaling properties an their related methodologies in mathematics, physics, mechanical and control engineering.
Reviewer: Vladimir Sobolev (Samara)Explicit symmetries of the Kepler Hamiltonianhttps://www.zbmath.org/1483.370662022-05-16T20:40:13.078697Z"Knörrer, Horst"https://www.zbmath.org/authors/?q=ai:knorrer.horstSummary: Using quaternions, we give explicit formulas for the global symmetries of the three-dimensional Kepler problem. The regularizations of the Kepler problem that are based on the Hopf map and on stereographic projections, respectively, are interpreted in terms of these symmetries.
For the entire collection see [Zbl 1456.14003].Hamiltonian pitchfork bifurcation in transition across index-1 saddleshttps://www.zbmath.org/1483.370682022-05-16T20:40:13.078697Z"Lyu, Wenyang"https://www.zbmath.org/authors/?q=ai:lyu.wenyang"Naik, Shibabrat"https://www.zbmath.org/authors/?q=ai:naik.shibabrat"Wiggins, Stephen"https://www.zbmath.org/authors/?q=ai:wiggins.stephenSummary: We study the effect of changes in the parameters of a two dimensional potential energy surface on the phase space structures relevant for chemical reaction dynamics. The changes in the potential energy are representative of chemical reactions such as isomerization between two structural conformations or dissociation of a molecule with an intermediate. We present a two degrees of freedom (DOF) quartic Hamiltonian that shows pitchfork bifurcation when the parameters are varied and we derive the bifurcation criteria relating the parameters. Next, we describe the phase space structures -- unstable periodic orbits and its associated invariant manifolds, and phase space dividing surfaces -- for the systems that can show trajectories undergo reaction defined as crossing of a potential energy barrier. Finally, we quantify the reaction dynamics for these systems by obtaining the directional flux and gap time distribution to illustrate the dependence on total energy and coupling strength between the two degrees of freedom.On the Lyapunov instability in Newtonian dynamicshttps://www.zbmath.org/1483.370692022-05-16T20:40:13.078697Z"Burgos, J. M."https://www.zbmath.org/authors/?q=ai:burgos.juan-manuel"Maderna, E."https://www.zbmath.org/authors/?q=ai:maderna.ezequiel"Paternain, M."https://www.zbmath.org/authors/?q=ai:paternain.miguelThe authors consider the classical problem of Lyapunov instability of equilibrium states for a finite-dimensional Newtonian system with a non-strict local minimum of the potential. For the cases when the local minimum of the potential energy is reached on the hypersurface of the configuration space, new results on the instability of equilibrium states are obtained.
Reviewer: Vladimir Sobolev (Samara)Geometrical classification of self-similar motion of two-dimensional three point vortex system by deviation curvature on Jacobi fieldhttps://www.zbmath.org/1483.370702022-05-16T20:40:13.078697Z"Hirakui, Yuma"https://www.zbmath.org/authors/?q=ai:hirakui.yuma"Yajima, Takahiro"https://www.zbmath.org/authors/?q=ai:yajima.takahiroSummary: In this study, we geometrically analyze the relation between a point vortex system and deviation curvatures on the Jacobi field. First, eigenvalues of deviation curvatures are calculated from relative distances of point vortices in a three point vortex system. Afterward, based on the assumption of self-similarity, time evolutions of eigenvalues of deviation curvatures are shown. The self-similar motions of three point vortices are classified into two types, expansion and collapse, when the relative distances vary monotonously. Then, we find that the eigenvalues of self-similarity are proportional to the inverse fourth power of relative distances. The eigenvalues of the deviation curvatures monotonically convergent to zero for expansion, whereas they monotonically diverge for collapse, which indicates that the strengths of interactions between point vortices related to the time evolution of spatial geometric structure in terms of the deviation curvatures. In particular, for collapse, the collision point becomes a geometric singularity because the eigenvalues of the deviation curvature diverge. These results show that the self-similar motions of point vortices are classified by eigenvalues of the deviation curvature. Further, nonself-similar expansion is numerically analyzed. In this case, the eigenvalues of the deviation curvature are nonmonotonous but converge to zero, suggesting that the motion of the nonself-similar three point vortex system is also classified by eigenvalues of the deviation curvature.Solvable dynamical systems in the plane with polynomial interactionshttps://www.zbmath.org/1483.370732022-05-16T20:40:13.078697Z"Calogero, Francesco"https://www.zbmath.org/authors/?q=ai:calogero.francesco-a"Payandeh, Farrin"https://www.zbmath.org/authors/?q=ai:payandeh.farrinSummary: In this paper we report a few examples of algebraically solvable dynamical systems characterized by \(2\) coupled Ordinary Differential Equations which read as follows:
\[
\dot{x}_n=P^{\left( n\right) }\left( x_1,x_2\right),\quad n=1,2,
\]
with \(P^{(n)}(x_1,x_2)\) specific polynomials of relatively low degree in the \(2\) dependent variables \(x_1\equiv x_1(t)\) and \(x_2\equiv x_2(t)\). These findings are obtained via a new twist of a recent technique to identify dynamical systems solvable by algebraic operations, themselves explicitly identified as corresponding to the time evolutions of the zeros of polynomials the coefficients of which evolve according to algebraically solvable (systems of) evolution equations.
For the entire collection see [Zbl 1456.14003].The rigid body dynamics in an ideal fluid: Clebsch top and Kummer surfaceshttps://www.zbmath.org/1483.370752022-05-16T20:40:13.078697Z"Françoise, Jean-Pierre"https://www.zbmath.org/authors/?q=ai:francoise.jean-pierre"Tarama, Daisuke"https://www.zbmath.org/authors/?q=ai:tarama.daisukeSummary: This is an expository presentation of a completely integrable Hamiltonian system of Clebsch top under a special condition introduced by Weber. After a brief account of the geometric setting of the system, the structure of the Poisson commuting first integrals is discussed following the methods by \textit{F. Magri} and \textit{T. Skrypnyk} [``The Clebsch System'', Preprint, \url{arXiv:1512.04872}]. Introducing supplementary coordinates, a geometric connection to Kummer surfaces, a typical class of K3 surfaces, is mentioned and also the system is linearized on the Jacobian of a hyperelliptic curve of genus two determined by the system. Further some special solutions contained in some vector subspace are discussed. Finally, an explicit computation of the action variables is introduced.
For the entire collection see [Zbl 1456.14004].Moser's theorem for hyperbolic-type degenerate lower tori in Hamiltonian systemhttps://www.zbmath.org/1483.370802022-05-16T20:40:13.078697Z"Jing, Tianqi"https://www.zbmath.org/authors/?q=ai:jing.tianqi"Si, Wen"https://www.zbmath.org/authors/?q=ai:si.wenThe main result of the paper is about the existence of lower-dimensional tori for a class of degenerate Hamiltonian systems, that are also supposed to be only \(C^\ell\) smooth. This is a generalization of known results for which the degenerate case was considered within the analytic class, or the loss of analyticity was considered in the non-degenerate case.
The proof is ruled out in the framework of KAM theory. The loss of regularity is overcome via the Jackson-Moser-Zehnder analytic approximation, while the degeneracy is treated through normal form theory for quasi-homogeneous polynomial systems and the stability of equilibrium points of odd degree polynomials.
Some applications of the main theorem are given.
Reviewer: Stefano Marò (Pisa)Adaptive Hamiltonian variational integrators and applications to symplectic accelerated optimizationhttps://www.zbmath.org/1483.370992022-05-16T20:40:13.078697Z"Duruisseaux, Valentin"https://www.zbmath.org/authors/?q=ai:duruisseaux.valentin"Schmitt, Jeremy"https://www.zbmath.org/authors/?q=ai:schmitt.jeremy-m"Leok, Melvin"https://www.zbmath.org/authors/?q=ai:leok.melvinSymplectic integrators with a variable stepsize usually do not preserve the energy. Nevertheless, the use of a variable stepsize could be useful in many instances. Motivated by these facts, the authors study the use of variable stepsize for specific classes of variational integrators. This is done by introducing a fictitious time \(\tau\), and defining an augmented Hamiltonian defined in terms of a ``monitor function'' which rules the time-step variation. The considered integrators turn out to be symplectic with constant time-step w.r.t. \(\tau\) and variable time-step w.r.t. the physical time \(t\). Applications to the Kepler problem and to accelerated optimization are presented.
Reviewer: Luigi Brugnano (Firenze)Ergodic decay laws in Newtonian and relativistic chaotic scatteringhttps://www.zbmath.org/1483.371032022-05-16T20:40:13.078697Z"Fernández, Diego S."https://www.zbmath.org/authors/?q=ai:fernandez.diego-s"López, Álvaro G."https://www.zbmath.org/authors/?q=ai:lopez.alvaro-g"Seoane, Jesús M."https://www.zbmath.org/authors/?q=ai:seoane.jesus-m"Sanjuán, Miguel A. F."https://www.zbmath.org/authors/?q=ai:sanjuan.miguel-a-fSummary: In open Hamiltonian systems, the escape from a bounded region of phase space according to an exponential decay law is frequently associated with the existence of hyperbolic dynamics in such a region. Furthermore, exponential decay laws based on the ergodic hypothesis are used to describe escapes in these systems. However, we uncover that the presence of the set that governs the hyperbolic dynamics, commonly known as the chaotic saddle, invalidates the assumption of ergodicity. For the paradigmatic Hénon-Heiles system, we use both theoretical and numerical arguments to show that the escaping dynamics is non-ergodic independently of the existence of KAM tori, since the chaotic saddle, in whose vicinity trajectories are more likely to spend a finite amount of time evolving before escaping forever, is not utterly spread over the energy shell. Taking this into consideration, we provide a clarifying discussion about ergodicity in open Hamiltonian systems and explore the limitations of ergodic decay laws when describing escapes in this kind of systems. Finally, we generalize our claims by deriving a new decay law in the relativistic regime for an inertial and a non-inertial reference frames under the assumption of ergodicity, and suggest another approach to the description of escape laws in open Hamiltonian systems.Equilibria and their stability in networks with steep sigmoidal nonlinearitieshttps://www.zbmath.org/1483.371072022-05-16T20:40:13.078697Z"Duncan, William"https://www.zbmath.org/authors/?q=ai:duncan.william"Gedeon, Tomas"https://www.zbmath.org/authors/?q=ai:gedeon.tomas"Kokubu, Hiroshi"https://www.zbmath.org/authors/?q=ai:kokubu.hiroshi"Mischaikow, Konstantin"https://www.zbmath.org/authors/?q=ai:mischaikow.konstantin"Oka, Hiroe"https://www.zbmath.org/authors/?q=ai:oka.hiroeOptimisation of controller reconfiguration instant for spacecraft control systems with additive actuator faultshttps://www.zbmath.org/1483.490082022-05-16T20:40:13.078697Z"Tu, Yuanyuan"https://www.zbmath.org/authors/?q=ai:tu.yuanyuan"Wang, Dayi"https://www.zbmath.org/authors/?q=ai:wang.dayi"Li, Wenbo"https://www.zbmath.org/authors/?q=ai:li.wenbo"Li, Maodeng"https://www.zbmath.org/authors/?q=ai:li.maodengSummary: This paper aims to propose a method of optimising the controller reconfiguration (CR) instant for spacecraft control systems with additive actuator faults. Due to severe resource constraints, it is `expensive' for spacecraft to handle the faults in orbit. To overcome the constraints, we try to reduce the CR cost from a perspective of time management. The basic idea of this method is to propose a reconfigurability evaluation index to quantify the capability of the fault system in maintaining admissible performance by CR measures, and then to derive the mathematical relationship between the reconfigurability index and four crucial instants during the CR process. Based on this, the CR instant is optimised by maximising the reconfigurability index. Finally, the effectiveness of the proposed method is illustrated through an example. The results show that by enhancing the time management efficiency during the CR process, the limited resources can be economised to some extent.High-order fully actuated system approaches. VIII: Optimal control with application in spacecraft attitude stabilisationhttps://www.zbmath.org/1483.490432022-05-16T20:40:13.078697Z"Duan, Guangren"https://www.zbmath.org/authors/?q=ai:duan.guangrenSummary: In this paper, the optimal control problem for dynamical systems represented by general high-order fully actuated (HOFA) models is formulated. The problem aims to minimise an objective in the quadratic form of the states and their derivatives of certain orders. The designed controller is a combination of the linearising nonlinear controller and an optimal quadratic controller for a converted linear system. In the infinite-time output regulation case, the solution is in essence a nonlinear state feedback dependent on a well-known Riccati algebraic equation. In the sub-fully actuated system case, the feasibility of the controller is investigated and guaranteed by properly characterising a ball restriction area of the system initial values. Application of the optimal control technique for sub-fully actuated systems to a spacecraft attitude control provides very smooth and steady responses and well demonstrates the effect and simplicity of the proposed approach.
For Part I--VII, see
[the auhor, ibid. 52, No. 2, 422--435 (2021; Zbl 1480.93184);
ibid. 52, No. 3, 437--454 (2021; Zbl 1480.93138);
ibid. 52, No. 5, 952--971 (2021; Zbl 1480.93096);
ibid. 52, No. 5, 972--989 (2021; Zbl 1480.93223);
ibid. 52, No. 10, 2129--2143 (2021; Zbl 1480.93097);
ibid. 52, No. 10, 2161--2181 (2021; Zbl 1480.93282);
ibid. 52, No. 14, 3091--3114 (2021; Zbl 1480.93038)].Pedal coordinates and free double linkagehttps://www.zbmath.org/1483.530042022-05-16T20:40:13.078697Z"Blaschke, Petr"https://www.zbmath.org/authors/?q=ai:blaschke.petr"Blaschke, Filip"https://www.zbmath.org/authors/?q=ai:blaschke.filip"Blaschke, Martin"https://www.zbmath.org/authors/?q=ai:blaschke.martinAuthors' abstract: A free double linkage is a mechanical system with three point-masses, two of which are linked to the central node by massless rigid rods. Using the technique of pedal coordinates the authors investigate the orbits of a free double linkage. They provide a geometrical construction for them and also show a surprising connection between this mechanical system and orbits around a Black Hole and solutions of the Dark Kepler problem.
Reviewer: Ergin Bayram (Samsun)The entropy of the angenent torus is approximately 1.85122https://www.zbmath.org/1483.531062022-05-16T20:40:13.078697Z"Berchenko-Kogan, Yakov"https://www.zbmath.org/authors/?q=ai:berchenko-kogan.yakovSummary: To study the singularities that appear in mean curvature flow, one must understand \textit{self-shrinkers}, surfaces that shrink by dilations under mean curvature flow. The simplest examples of self-shrinkers are spheres and cylinders. In [Prog. Nonlinear Differ. Equ. Appl. 7, 21--38 (1992; Zbl 0762.53028)], \textit{S. B. Angenent} constructed the first nontrivial example of a self-shrinker, a torus. A key quantity in the study of the formation of singularities is the \textit{entropy}, defined by Colding and Minicozzi based on work of Huisken. The values of the entropy of spheres and cylinders have explicit formulas, but there is no known formula for the entropy of the Angenent torus. In this work, we numerically estimate the entropy of the Angenent torus using the discrete Euler-Lagrange equations.A curve shortening equation with time-dependent mobility related to grain boundary motionshttps://www.zbmath.org/1483.531092022-05-16T20:40:13.078697Z"Mizuno, Masashi"https://www.zbmath.org/authors/?q=ai:mizuno.masashi"Takasao, Keisuke"https://www.zbmath.org/authors/?q=ai:takasao.keisukeSummary: A curve shortening equation related to the evolution of grain boundaries is presented. This equation is derived from the grain boundary energy by applying the maximum dissipation principle. Gradient estimates and large time asymptotic behavior of solutions are considered. In the proof of these results, one key ingredient is a new weighted monotonicity formula that incorporates a time-dependent mobility.Incompressible viscous fluids in \(\mathbb{R}^2\) and SPDEs on graphs, in presence of fast advection and non smooth noisehttps://www.zbmath.org/1483.600902022-05-16T20:40:13.078697Z"Cerrai, Sandra"https://www.zbmath.org/authors/?q=ai:cerrai.sandra"Xi, Guangyu"https://www.zbmath.org/authors/?q=ai:xi.guangyuSummary: The asymptotic behavior of a class of stochastic reaction-diffusion-advection equations in the plane is studied. We show that as the divergence-free advection term becomes larger and larger, the solutions of such equations converge to the solution of a suitable stochastic PDE defined on the graph associated with the Hamiltonian. Firstly, we deal with the case that the stochastic perturbation is given by a singular spatially homogeneous Wiener process taking values in the space of Schwartz distributions. As in previous works, we assume here that the derivative of the period of the motion on the level sets of the Hamiltonian does not vanish. Then, in the second part, without assuming this condition on the derivative of the period, we study a weaker type of convergence for the solutions of a suitable class of linear SPDEs.A high order finite difference weighted essentially nonoscillatory schemes with a kernel-based constrained transport method for ideal magnetohydrodynamicshttps://www.zbmath.org/1483.651302022-05-16T20:40:13.078697Z"Cakir, Firat"https://www.zbmath.org/authors/?q=ai:cakir.firat"Christlieb, Andrew"https://www.zbmath.org/authors/?q=ai:christlieb.andrew-j"Jiang, Yan"https://www.zbmath.org/authors/?q=ai:jiang.yanThe ideal magnetohydrodynamics (MHD) equations are considered. While the MHD equations are hyperbolic, standard numerical methods for hyperbolic conservation laws fail to guarantee \(\nabla \cdot B = 0\). In this work, a new high order method to satisfy the involution based on an unstaggered constrained transport (CT) methodology is introduced. The paper is organized as follows. Section 1 is an introduction. In Section 2, the MHD equations, CT method, and the evolution of the magnetic vector equations are briefly reviewed. In Section 3, the novel numerical scheme for 1D Hamilton-Jacobi equations and the multidimensional solver are presented. The resulting 2D and 3D schemes are tested on several numerical problems, in Section 4. In this section, the numerical results are presented to demonstrate the accuracy and efficiency of the constructed algorithm. In Section 5, some conclusions are given. Finally, in Appendix A, all coefficients in weighted essentially nonoscillatory quadrature are shown.
Reviewer: Temur A. Jangveladze (Tbilisi)Feedback integrators for nonholonomic mechanical systemshttps://www.zbmath.org/1483.652022022-05-16T20:40:13.078697Z"Chang, Dong Eui"https://www.zbmath.org/authors/?q=ai:chang.dong-eui"Perlmutter, Matthew"https://www.zbmath.org/authors/?q=ai:perlmutter.matthewSummary: The theory of feedback integrators is extended to handle mechanical systems with nonholonomic constraints with or without symmetry, so as to produce numerical integrators that preserve the nonholonomic constraints as well as other conserved quantities. To extend the feedback integrators, we develop a suitable extension theory for nonholonomic systems and also a corresponding reduction theory for systems with symmetry. It is then applied to various nonholonomic systems such as the Suslov problem on \(\mathrm{SO}(3)\), the knife edge, the Chaplygin sleigh, the vertical rolling disk, the roller racer, the Heisenberg system, and the nonholonomic oscillator.Planetary giant impacts. Simulating collisions and their consequenceshttps://www.zbmath.org/1483.700012022-05-16T20:40:13.078697Z"Kegerreis, Jacob"https://www.zbmath.org/authors/?q=ai:kegerreis.jacobThe Ph. D. thesis contains six chapters. The first chapter is introductory in nature and explains about the work done in the subsequent chapters. The last chapter contains the concluding remarks and the future work. The remaining four chapters contain the work done by the candidate in his Ph D time. The Ph D thesis provides significant progress with both of these aspects of simulation work, presenting a new method for placing particles into spherically symmetric objects in a way that reduces transient disequilibrium behaviour, and adapting the very efficient SWIFT (SPH With Inter-dependent Fine-grained Tasking) open-source software for planetary giant impact simulations. This thesis uses these new methods to investigate what type of impacting body could have led to Uranus' rotation axis lying almost in the plane of the solar system. The distribution of impactor material within the post-impact planet and the composition of the mass placed into orbit are accessible to the high resolution simulations presented here.
Reviewer: P. K. Sahoo (Hyderabad)Analysis of the dymamic equilibrium conditions for the symmetry axis of an artillery shellhttps://www.zbmath.org/1483.700022022-05-16T20:40:13.078697Z"Konosevich, B. I."https://www.zbmath.org/authors/?q=ai:konosevich.b-i"Konosevich, Yu. B."https://www.zbmath.org/authors/?q=ai:konosevich.yu-b"Mozalevskaya, G. V."https://www.zbmath.org/authors/?q=ai:mozalevskaya.g-vSummary: Motion of a fast spinning artillery shell as a rigid body is described in the article by an ODE system, where expressions of aerodynamic forces and moments are taken, which are linearized in the total angle of attack. It is shown that the definition of the dymamic equilibrium position of the symmetry axis of the shell, proposed by R. Lieske and M. Reiter, differs from its definition as a quasi-stationary solution of the equations of angular motion of the symmetry axis only by the lack of the pitch damping moment coefficient.Dynamics of a spherical robot with variable moments of inertia and a displaced center of masshttps://www.zbmath.org/1483.700032022-05-16T20:40:13.078697Z"Artemova, Elizaveta M."https://www.zbmath.org/authors/?q=ai:artemova.elizaveta-m"Karavaev, Yury L."https://www.zbmath.org/authors/?q=ai:karavaev.yuri-leonidovich"Mamaev, Ivan S."https://www.zbmath.org/authors/?q=ai:mamaev.ivan-s"Vetchanin, Evgeny V."https://www.zbmath.org/authors/?q=ai:vetchanin.evgenii-vladimirovichSummary: The motion of a spherical robot with periodically changing moments of inertia, internal rotors and a displaced center of mass is considered. It is shown that, under some restrictions on the displacement of the center of mass, the system of interest features chaotic dynamics due to separatrix splitting. A stability analysis is made of the upper equilibrium point of the ball and of the periodic solution arising in its neighborhood, in the case of periodic rotation of the rotors. It is shown that the lower equilibrium point can become unstable in the case of fixed rotors and periodically changing moments of inertia.Linear-time variational integrators in maximal coordinateshttps://www.zbmath.org/1483.700042022-05-16T20:40:13.078697Z"Brüdigam, Jan"https://www.zbmath.org/authors/?q=ai:brudigam.jan"Manchester, Zachary"https://www.zbmath.org/authors/?q=ai:manchester.zacharySummary: Most dynamic simulation tools parameterize the configuration of multi-body robotic systems using minimal coordinates, also called generalized or joint coordinates. However, maximal-coordinate approaches have several advantages over minimal-coordinate parameterizations, including native handling of closed kinematic loops and nonholonomic constraints. This paper describes a linear-time variational integrator that is formulated in maximal coordinates. Due to its variational formulation, the algorithm does not suffer from constraint drift and has favorable energy and momentum conservation properties. A sparse matrix factorization technique allows the dynamics of a loop-free articulated mechanism with nlinks to be computed in \(O(n)\) (linear) time. Additional constraints that introduce loops can also be handled by the algorithm without incurring much computational overhead. Experimental results show that our approach offers speed competitive with state-of-the-art minimal-coordinate algorithms while outperforming them in several scenarios, especially when dealing with closed loops and configuration singularities.
For the entire collection see [Zbl 1464.68013].A Gough-Stewart parallel manipulator with configurable platform and multiple end-effectorshttps://www.zbmath.org/1483.700052022-05-16T20:40:13.078697Z"Gallardo-Alvarado, Jaime"https://www.zbmath.org/authors/?q=ai:gallardo-alvarado.jaimeSummary: This work describes a novel robot manipulator with configurable platform. Three internal degrees-of-freedom are added for controlling the relative orientation of the terminal links supporting multiple end-effectors of a Gough-Stewart-type parallel manipulator. The instantaneous forward and inverse kinematic analyses of the robot are derived using the theory of screws. Furthermore, the exploitation of this approach for deriving the acceleration analyses of a parallel manipulator with configurable platform is novel in this research field. As an intermediate step the forward and inverse displacement analyses are also investigated. A numerical example is compared with the outcome of a commercial software demonstrating the approach correctness.Optimum dimensional synthesis of planar mechanisms with geometric constraintshttps://www.zbmath.org/1483.700062022-05-16T20:40:13.078697Z"García-Marina, V."https://www.zbmath.org/authors/?q=ai:garcia-marina.v"Fernández de Bustos, I."https://www.zbmath.org/authors/?q=ai:fernandez-de-bustos.i"Urkullu, G."https://www.zbmath.org/authors/?q=ai:urkullu.g"Ansola, R."https://www.zbmath.org/authors/?q=ai:ansola.rubenSummary: The deformed energy method has shown to be a good option for dimensional synthesis of mechanisms. In this paper the introduction of some new features to such approach is proposed. First, constraints fixing dimensions of certain links are introduced in the error function of the synthesis problem. Second, requirements on distances between determinate nodes are included in the error function for the analysis of the deformed position problem. Both the overall synthesis error function and the inner analysis error function are optimized using a Sequential Quadratic Problem (SQP) approach. This also reduces the probability of branch or circuit defects. In the case of the inner function analytical derivatives are used, while in the synthesis optimization approximate derivatives have been introduced. Furthermore, constraints are analyzed under two formulations, the Euclidean distance and an alternative approach that uses the previous raised to the power of two. The latter approach is often used in kinematics, and simplifies the computation of derivatives. Some examples are provided to show the convergence order of the error function and the fulfilment of the constraints in both formulations studied under different topological situations or achieved energy levels.A new human-like walking for the humanoid robot \textit{Romeo}https://www.zbmath.org/1483.700072022-05-16T20:40:13.078697Z"Kalouguine, A."https://www.zbmath.org/authors/?q=ai:kalouguine.a"De-León-Gómez, V."https://www.zbmath.org/authors/?q=ai:de-leon-gomez.v"Chevallereau, C."https://www.zbmath.org/authors/?q=ai:chevallereau.christine"Dalibard, S."https://www.zbmath.org/authors/?q=ai:dalibard.s"Aoustin, Y."https://www.zbmath.org/authors/?q=ai:aoustin.yannickSummary: This paper seeks to define the anthropomorphic walking motion for the humanoid robot \textit{Romeo}. The main characteristics of the lower and upper limb motions of the human being during walking are adapted to \textit{Romeo} taking into account its kinematics and its motor power. The proposed walking includes starting, periodic and stopping motions. A boundary value problem is stated and solved to define each of these three movements, which are composed of single and double support phases. The trajectory of the zero moment point (\textit{ZMP}) is explicitly defined as a function of time. Thanks to the \textit{Essential model}, the two horizontal coordinates of the center of mass (\textit{CoM}) are adapted to the desired \textit{ZMP} trajectory and joint movements of \textit{Romeo}. Numerical results show the efficiency of our strategy to design human-like walking for \textit{Romeo}.A general spatial multi-loop linkage optimization model for motion generation with static loadinghttps://www.zbmath.org/1483.700082022-05-16T20:40:13.078697Z"Lee, Wen-Tzong"https://www.zbmath.org/authors/?q=ai:lee.wen-tzong"Shen, Qiong"https://www.zbmath.org/authors/?q=ai:shen.qiong"Russell, Kevin"https://www.zbmath.org/authors/?q=ai:russell.kevinIn this article the authors present an optimization routine for particular types of spatial linkages. They focus on the so-called RSSR-SS linkage whose architecture is as follows: The end-effector is connected to the base by three legs which have spherical joints on their end-effector ends. On their base ends only one of the legs has a spherical joint whereas the other two have revolute joints. Due to this architecture the motion of the end-effector with respect to the base is only 1-parametric. Hence, one of the revolute joint angles (called \(\theta\) subsequently) can be chosen to parameterize this motion: A single motor driving this revolute joint will control the end-effector motion.
The input for the optimization routine consists of a number of prescribed poses \(\mathbf{p}_j^\ast, \mathbf{q}_j^\ast, \mathbf{r}_j^\ast\), \(j=2,\dots, N\) of 3 points \(\mathbf{p}, \mathbf{q}, \mathbf{r}\) of the linkage's end-effector. The objective function \(f\) (function to be minimized) can then be written as \[f(\mathbf{X}) \;\,:= \;\, \sum_{j=2}^N \left(\| \mathbf{p}_j^\ast - \mathbf{p}_j\|^2 + \| \mathbf{q}_j^\ast - \mathbf{q}_j\|^2 + \| \mathbf{r}_j^\ast - \mathbf{r}_j\|^2 \right)\] where \(\mathbf{p}_j, \mathbf{q}_j, \mathbf{r}_j\), \(j=2,\dots, N\) denote the positions of \(\mathbf{p}, \mathbf{q}, \mathbf{r}\) by the synthesized RSSR-SS linkage. \(f\) is a function of the design variables which are
\begin{itemize}
\item the position vectors of the six leg endpoints,
\item the direction vectors of the two revolute joints' axes,
\item and the values \(\theta_j\), \(j=2,\dots, N\) of the driving angle \(\theta\) belonging to poses of the driven leg.
\end{itemize}
A small value of \(f\) would give an RSSR-SS linkage which fairly approximates the prescribed poses.
Of course, the authors have to involve quite a bunch of side conditions on these design variables. On the one hand there are \textit{equality constraints} involving constant distance of points throughout the motion, orthogonality and unit-vector constraints. But there are also many \textit{inequality constraints} for eliminating branch effects and order defects. Additionally, the authors add inequalities controlling torque restriction.
Examples generated via MATLAB based on the so-called \textit{interior-point algorithm} for solving the discussed nonlinear optimization task are also presented in the paper. The authors report that even for the case of only two prescribed poses the computations produce large file sizes and are therefore rather impracticable on standard computers.
Reviewer: Anton Gfrerrer (Graz)Stiffness model reduction for manipulators with double encoders: algebraic approachhttps://www.zbmath.org/1483.700092022-05-16T20:40:13.078697Z"Mikhel, S. K."https://www.zbmath.org/authors/?q=ai:mikhel.s-k"Klimchik, A. S."https://www.zbmath.org/authors/?q=ai:klimchik.alexandr-sSummary: The accuracy of the robot positioning during material processing can be improved if the deformation under the load is taken into account. A manipulator stiffness model can be obtained using various approaches which differ in the degree of detail and computational complexity. Regardless of the model, its practical application requires knowledge of the stiffness parameters of the robot components, which implies solving the identification problem.
In this work, we consider a reduced stiffness model, which assumes that the manipulator links are rigid, while the joints are compliant and include both elasticities in the joints themselves and the elastic properties of the links. This simplification reduces the accuracy of the model, but allows us to identify the stiffness parameters, which makes it suitable for practical application. In combination with a double encoders measurement system, this model allows for real-time compensation of compliance errors, that is, the deviation of the real end-effector position from the calculated one due to the deformation of the robot under load.
The paper proposes an algebraic approach to determining the parameters of the reduced model in a general form. It also demonstrates several steps that can be done to simplify computations. First, it introduces the backward semianalytical Jacobian computation technique, which allows reducing the number of operations for the manipulator with virtual joints. Second, it provides an algorithm for the calculation of the required intermediate matrices without explicit Jacobian calculation and using more compact expressions.
To compare the proposed techniques with the experimental approach, the robot deformation under load is simulated and the tool displacement is estimated. It is shown that both approaches are equivalent in terms of accuracy. While the experimental method is easier to implement, the algebraic approach allows analyzing the contribution of each link in a reduced model of elasticity. Besides, the obtained estimate of the parameters does not depend on the accuracy of measurements and configurations used in the identification process.A synthesis method for path generation of a planar five-bar mechanism based on dynamic self-adaptive atlas databasehttps://www.zbmath.org/1483.700102022-05-16T20:40:13.078697Z"Sun, Jianwei"https://www.zbmath.org/authors/?q=ai:sun.jianwei"Xue, Na"https://www.zbmath.org/authors/?q=ai:xue.na"Liu, Wenrui"https://www.zbmath.org/authors/?q=ai:liu.wenrui"Chu, Jinkui"https://www.zbmath.org/authors/?q=ai:chu.jinkuiSummary: A method for the path synthesis of a planar five-bar mechanism based on wavelet analysis theory is proposed in this paper. Wavelet transform analysis is used to extract wavelet characteristic parameters (WCPs) from the basic dimensional types (BDTs) database. Combined the numerical atlas method with multidimensional search tree, a four dimensions search tree with a depth of five is obtained, in which numbers of leaf nodes are 4,096, and each node stores 59,787 groups of BDTs database numbers. Meanwhile, an index keyword database is established. By comparing the WCPs of a prescribed curve with index keywords, the leaf node where the desired mechanism is located is found. The WCPs of the BDTs in the leaf node are extracted, and a dynamic self-adaptive atlas database is established. Based on the design requirements, the desired mechanism can be obtained by fuzzy identification. Then, a mathematical model is established for calculating the actual sizes of the desired mechanism. The arbitrary design interval path synthesis of a five-bar mechanism is realized. Two examples are presented to demonstrate the veracity and practicality of the method proposed.Searching for equilibrium states of Atwood's machine with two oscillating bodies by means of computer algebrahttps://www.zbmath.org/1483.700112022-05-16T20:40:13.078697Z"Prokopenya, A. N."https://www.zbmath.org/authors/?q=ai:prokopenya.alexander-nSummary: In this paper, we discuss the problem of searching for equilibrium states of Atwood's machine in which a pulley of a finite radius is replaced by two separate small pulleys and both masses can oscillate in a vertical plane. Differential equations of motion for the system are derived, and their solutions are computed in the form of power series in a small parameter. It is shown that, in the case of equal masses, the equilibrium position \(r = {\text{const}}\) of the system exists only if the oscillation amplitudes and frequencies of the masses are the same and the phase shift is \(\alpha = 0\) or \(\alpha = \pi \). In addition, there is a dynamic equilibrium state when both masses oscillate with the same amplitudes and frequencies and the phase shift is \(\alpha = \pm \pi/2\). In this case, the lengths of the pendulums also oscillate around a certain equilibrium value. Comparison of the results with the corresponding numerical solutions of the motion equations confirms their correctness. All necessary computations are carried out using the Wolfram Mathematica computer algebra system.A note on the Lyapunov stability of linear conservative gyroscopic systemshttps://www.zbmath.org/1483.700122022-05-16T20:40:13.078697Z"Bulatovic, Ranislav M."https://www.zbmath.org/authors/?q=ai:bulatovic.ranislav-mSummary: The stability of linear conservative gyroscopic systems with a degenerate potential matrix is considered. First, using a Lyapunov-type approach, a simple necessary and sufficient condition for stability of the systems with positive semi-definite potential matrices is derived. After that, a generalization of the famous Kelvin-Tait-Chetaev theorem is given, which covers the degenerate case.The investigation of motions of the symmetric gyrostat with fixed point in the case of variable gyrostatic momenthttps://www.zbmath.org/1483.700132022-05-16T20:40:13.078697Z"Kotov, G. A."https://www.zbmath.org/authors/?q=ai:kotov.g-a"Pilpani, Yu. Yu."https://www.zbmath.org/authors/?q=ai:pilpani.yu-yuSummary: Existence conditions are studied for precession motions of a gyrostat with one non-uniformly rotating rotor in the cases, when epy gyrostat moves in the gravity field or under the action of potential forces. On the basis of analysis of equations of motion, an expression is written for the gyrostatic moment, which allows to derive three first integrals for the system of equations of motion. By means of methods, using for solving the inverse problems of mechanics, a forcing function is constructed on the invariant relations describing precessions of the general type, and a forcing function characterizing the speed of proper rotation of the body is build.Some problems of attitude dynamics and control of a rigid bodyhttps://www.zbmath.org/1483.700142022-05-16T20:40:13.078697Z"Aleksandrov, A. Yu."https://www.zbmath.org/authors/?q=ai:aleksandrov.aleksandr-yurevich"Martynyuk, A. A."https://www.zbmath.org/authors/?q=ai:martynyuk.anatoly-a"Tikhonov, A. A."https://www.zbmath.org/authors/?q=ai:tikhonov.aleksei-aleksandrovichSummary: In the present paper, Vladimir Zubov's results on the problems of analysis and control of rotation motion of a rigid body are surveyed together with their developments and extensions.Constant-speed ramps for a central force fieldhttps://www.zbmath.org/1483.700152022-05-16T20:40:13.078697Z"López, Rafael"https://www.zbmath.org/authors/?q=ai:lopez-camino.rafael"Perdomo, Óscar"https://www.zbmath.org/authors/?q=ai:perdomo.oscar-marioSummary: We investigate the problem of determining the planar curves that describe ramps where a particle of mass \(m\) moves with constant-speed when is subject to the action of the friction force and a force whose magnitude \(F(r)\) depends only on the distance \(r\) from the origin. In this paper we describe all the constant-speed ramps for the case \(F(r)=-m/r\). We show the circles and the logarithmic spirals play an important role. Not only they are solutions but every other solution approaches either a circle or a logarithmic spiral.The stability of the model and simulation, control issues for ship system, education, and researchhttps://www.zbmath.org/1483.700162022-05-16T20:40:13.078697Z"Danh, Nguyen Cong"https://www.zbmath.org/authors/?q=ai:danh.nguyen-congSummary: This article deals with the study of mathematical models and the assessment of the stability of the motion of ships, investigating properties of the system such as kinetics and stability. This is essential for the selection of suitable control methods according to the requirements set out for the problem. Some control methods require the author to specify control parameters before the operation of the system can be started. Therefore, the survey of the article is useful for the above problem. Control methods through simulation results (PID controller, lag compensator, and lead compensator) give me results that reflect properties of the system (the stability of the operation cycle of the ship model). In addition, control methods for this model, which serve for research and education, are also presented below. Simulation is done by Matlab.Stability of rigid body motion through an extended intermediate axis theorem: application to rockfall simulationhttps://www.zbmath.org/1483.700172022-05-16T20:40:13.078697Z"Leine, Remco I."https://www.zbmath.org/authors/?q=ai:leine.remco-i"Capobianco, Giuseppe"https://www.zbmath.org/authors/?q=ai:capobianco.giuseppe"Bartelt, Perry"https://www.zbmath.org/authors/?q=ai:bartelt.perry"Christen, Marc"https://www.zbmath.org/authors/?q=ai:christen.marc"Caviezel, Andrin"https://www.zbmath.org/authors/?q=ai:caviezel.andrinSummary: The stability properties of a freely rotating rigid body are governed by the intermediate axis theorem, i.e., rotation around the major and minor principal axes is stable whereas rotation around the intermediate axis is unstable. The stability of the principal axes is of importance for the prediction of rockfall. Current numerical schemes for 3D rockfall simulation, however, are not able to correctly represent these stability properties. In this paper an extended intermediate axis theorem is presented, which not only involves the angular momentum equations but also the orientation of the body, and we prove the theorem using Lyapunov's direct method. Based on the stability proof, we present a novel scheme which respects the stability properties of a freely rotating body and which can be incorporated in numerical schemes for the simulation of rigid bodies with frictional unilateral constraints. In particular, we show how this scheme is incorporated in an existing 3D rockfall simulation code. Simulations results reveal that the stability properties of rotating rocks play an essential role in the run-out length and lateral spreading of rocks.Stability analysis of a waveboard multibody model with toroidal wheelshttps://www.zbmath.org/1483.700182022-05-16T20:40:13.078697Z"Agúndez, A. G."https://www.zbmath.org/authors/?q=ai:agundez.a-g"García-Vallejo, D."https://www.zbmath.org/authors/?q=ai:garcia-vallejo.daniel"Freire, E."https://www.zbmath.org/authors/?q=ai:freire.eduarda-s-v|freire-macias.emilio|freire.eduardo-o|freire.elisabete"Mikkola, A. M."https://www.zbmath.org/authors/?q=ai:mikkola.aki-mSummary: This paper analyses the stability of a waveboard, the skateboard consisting in two articulated platforms, coupled by a torsion bar and supported of two caster wheels. The waveboard presents an interesting propelling mechanism, since the rider can achieve a forward motion by means of an oscillatory lateral motion of the platforms. In this paper, the system is described using a multibody model with nonholonomic constraints.
To study the stability of the forward upright motion with constant speed, the equations of motion are linearized with respect to a reference motion. The employed numerical linearization procedure is valid for general multibody systems with holonomic and nonholonomic constraints. In practice, the employed approach makes use of the Jacobian matrix, which is expressed in terms of any of the main design parameters of the waveboard. This paper introduces a sensitivity analysis of the eigenvalues with respect to the forward speed, the casters' inclination angle, the torsional stiffness of the torsion bar, the aspect ratio of the toroidal wheels and the mass of the human rider. Lastly, a summary with the influence of these design parameters on the external actuations exerted by the rider in the waveboard maneuvering is shown.Deep learning of multibody minimal coordinates for state and input estimation with Kalman filteringhttps://www.zbmath.org/1483.700192022-05-16T20:40:13.078697Z"Angeli, Andrea"https://www.zbmath.org/authors/?q=ai:angeli.andrea"Desmet, Wim"https://www.zbmath.org/authors/?q=ai:desmet.wim"Naets, Frank"https://www.zbmath.org/authors/?q=ai:naets.frankSummary: In general, multibody models are described with a set of redundant coordinates and additional constraints. Their dynamics is thus expressed through differential algebraic equations. As an alternative, the minimal coordinate formulation permits to describe a rigid system with the minimal number of variables leading to ordinary differential equations which can be employed in a coupled state/input estimation scheme. However, in some cases the explicit relation between the full-system coordinates and the minimal coordinates may not be available or analytically obtainable, as for closed-loop mechanisms. In this work, a previously presented deep learning framework to find the non-linear mapping and reduce a generic multibody model from redundant to minimal coordinates is employed. The resulting equations are then exploited in an extended Kalman filter where the unknown inputs are considered as augmented states and jointly estimated. The necessary derivatives are given and it is shown that acceleration measurements are sufficient for the estimation. The method is experimentally validated on a slider-crank mechanism.Global modes for the reduction of flexible multibody systems. Methodology and complexityhttps://www.zbmath.org/1483.700202022-05-16T20:40:13.078697Z"Cammarata, Alessandro"https://www.zbmath.org/authors/?q=ai:cammarata.alessandroSummary: Modeling a flexible multibody system employing the floating frame of reference formulation (FFRF) requires significant computational resources when the flexible components are represented through finite elements. Reducing the complexity of the governing equations of motion through component-level reduced-order models (ROM) can be an effective strategy. Usually, the assumed field of deformation is created considering local modes, such as normal, static, or attachment modes, obtained from a single component. A different approach has been proposed in [\textit{A. Cammarata}, ``Global flexible modes for the model reduction of planar mechanisms using the finite-element floating frame of reference formulation'', J. Sound Vib. 489, Article ID 115668, (2020; \url{doi:10.1016/j.jsv.2020.115668})] for planar systems only and involves a reduction based on global flexible modes of the whole mechanism. Through the use of global modes, i.e., obtained from an eigenvalue analysis performed on the linearized dynamic system around a certain configuration, it is possible to obtain a modal basis for the flexible coordinates of the multibody system. Here, the same method is extended to spatial mechanisms to verify its applicability and reliability. It is demonstrated that global modes can be used to create ROM both at the system and component levels. Studies on the complexity of the method reveal this approach can significantly reduce the calculation times and the computational effort compared to the unreduced model. Unlike the planar case, the numerical experiments reveal that the system-level approach based on global modes can suffer from slow convergence speed and low accuracy in results.Augmented Lagrangian index-3 semi-recursive formulations with projections. Kinematics and dynamicshttps://www.zbmath.org/1483.700212022-05-16T20:40:13.078697Z"Dopico Dopico, Daniel"https://www.zbmath.org/authors/?q=ai:dopico.daniel-dopico"López Varela, Álvaro"https://www.zbmath.org/authors/?q=ai:lopez-varela.alvaro"Luaces Fernández, Alberto"https://www.zbmath.org/authors/?q=ai:luaces-fernandez.albertoSummary: MBSLIM (Multibody Systems at Laboratorio de Ingenieria Mecanica) multibody library includes some global formulations for the dynamics and sensitivity analysis of multibody systems. The extension of the library to accommodate topological formulations in relative (joint) coordinates and their implementation are going to be described in two separate works, this one being devoted to dynamics and the second one to a sensitivity analysis. With this extension in the scope, some topological semi-recursive formulations derived in the past are revisited, generalized and reformulated. The need for generalization of the previously published formulations was detected because the equations proposed were not general enough to be integrated in an all-purpose multibody library in natural coordinates like MBSLIM, especially because both set of coordinates need to coexist, the definition of the mechanisms has to be the original one and the library has to be automatic and all the existing models have to work with the new approach. Moreover the new solver takes advantage of some problems solved in natural coordinates, like the initial position and initial velocity problems for closed-loop systems. Finally, to test the new equations, two benchmark problems are presented and their results compared: a spatial slider-crank mechanism and a buggy vehicle model.Dynamics of a flexible body: a two-field formulationhttps://www.zbmath.org/1483.700222022-05-16T20:40:13.078697Z"Géradin, Michel"https://www.zbmath.org/authors/?q=ai:geradin.michelSummary: A two-field formulation of the nonlinear dynamics of an elastic body is presented in which positions/orientations and the resulting velocity field are treated as independent. Combining a nonclassical description of elastic velocity that includes the convection velocity due to elastic deformation with floating reference axes minimizing the relative kinetic energy due to elastic deformation provides a fully uncoupled expression of kinetic energy. A transformation inspired by the classical Legendre transformation concept is introduced to develop the motion equations in canonical form. Finite element discretization is achieved using the same shape function sets for elastic displacements and velocities. Specific attention is brought to the discretization of the gyroscopic forces induced by elastic deformation. A model reduction strategy to construct superelement models suitable for flexible multibody dynamics applications is proposed, which fulfills the essential condition of orthogonality between a rigid body and elastic motions. The problem of expressing kinematic connections at superelement boundaries is briefly addressed. Two academic examples have been developed to illustrate some of the concepts presented.A review of flexible multibody dynamics for gradient-based design optimizationhttps://www.zbmath.org/1483.700232022-05-16T20:40:13.078697Z"Gufler, Veit"https://www.zbmath.org/authors/?q=ai:gufler.veit"Wehrle, Erich"https://www.zbmath.org/authors/?q=ai:wehrle.erich"Zwölfer, Andreas"https://www.zbmath.org/authors/?q=ai:zwolfer.andreasSummary: Design optimization of flexible multibody dynamics is critical to reducing weight and therefore increasing efficiency and lowering costs of mechanical systems. Simulation of flexible multibody systems, though, typically requires high computational effort which limits the usage of design optimization, especially when gradient-free methods are used and thousands of system evaluations are required. Efficient design optimization of flexible multibody dynamics is enabled by gradient-based optimization methods in concert with analytical sensitivity analysis. The present study summarizes different formulations of the equations of motion of flexible multibody dynamics. Design optimization techniques are introduced, and applications to flexible multibody dynamics are categorized. Efficient sensitivity analysis is the centerpiece of gradient-based design optimization, and sensitivity methods are introduced. The increased implementation effort of analytical sensitivity analysis is rewarded with high computational efficiency. An exemplary solution strategy for system and sensitivity evaluations is shown with the analytical direct differentiation method. Extensive literature sources are shown related to recent research activities.On design sensitivities in the structural analysis and optimization of flexible multibody systemshttps://www.zbmath.org/1483.700242022-05-16T20:40:13.078697Z"Held, Alexander"https://www.zbmath.org/authors/?q=ai:held.alexanderSummary: The structural analysis and optimization of flexible multibody systems become more and more popular due to the ability to efficiently compute gradients using sophisticated approaches such as the adjoint variable method and the adoption of powerful methods from static structural optimization. To drive the improvement of the optimization process, this work addresses the computation of design sensitivities for multibody systems with arbitrarily parameterized rigid and flexible bodies that are modeled using the floating frame of reference formulation. It is shown that it is useful to augment the body describing standard input data files by their design derivatives. In this way, a clear separation can be achieved between the body modeling and parameterization and the system simulation and analysis.Efficient formulation of the Gibbs-Appell equations for constrained multibody systemshttps://www.zbmath.org/1483.700252022-05-16T20:40:13.078697Z"Mirtaheri, S. M."https://www.zbmath.org/authors/?q=ai:mirtaheri.s-m"Zohoor, Hassan"https://www.zbmath.org/authors/?q=ai:zohoor.hassanSummary: In this study, we present explicit equations of motion for general mechanical systems exposed to holonomic and nonholonomic constraints based on the Gibbs-Appell formulation. Without constructing the Gibbs function, the proposed method provides a minimal set of first-order dynamic equations applicable for multibody constrained systems. Transforming the Newton-Euler equations from physical coordinates to quasivelocity spaces eliminate constraint reaction forces from motion equations. In this study, we develop a general procedure to select effective quasivelocities, which indicate that the proposed quasivelocities satisfy constraints, eliminate Lagrange multipliers, and reduce the number of dynamic equations to degrees of freedom. Besides, we test the validity and efficiency of the proposed approach using three constrained dynamical systems as illustrative examples. Finally, we compare the simulation results with Udwadia-Kalaba, augmented Lagrangian, and other conventional methods.Closed-form time derivatives of the equations of motion of rigid body systemshttps://www.zbmath.org/1483.700262022-05-16T20:40:13.078697Z"Müller, Andreas"https://www.zbmath.org/authors/?q=ai:muller.andreas-h|muller.andreas.1|muller.andreas|muller.andreas.2|muller.andreas-christian"Kumar, Shivesh"https://www.zbmath.org/authors/?q=ai:kumar.shiveshSummary: Derivatives of equations of motion (EOM) describing the dynamics of rigid body systems are becoming increasingly relevant for the robotics community and find many applications in design and control of robotic systems. Controlling robots, and multibody systems comprising elastic components in particular, not only requires smooth trajectories but also the time derivatives of the control forces/torques, hence of the EOM. This paper presents the time derivatives of the EOM in closed form up to second-order as an alternative formulation to the existing recursive algorithms for this purpose, which provides a direct insight into the structure of the derivatives. The Lie group formulation for rigid body systems is used giving rise to very compact and easily parameterized equations.Flexible multibody impact simulations based on the isogeometric analysis approachhttps://www.zbmath.org/1483.700272022-05-16T20:40:13.078697Z"Rückwald, Tobias"https://www.zbmath.org/authors/?q=ai:ruckwald.tobias"Held, Alexander"https://www.zbmath.org/authors/?q=ai:held.alexander"Seifried, Robert"https://www.zbmath.org/authors/?q=ai:seifried.robertSummary: Usually detailed impact simulations are based on isoparametric finite element models. For the inclusion in multibody dynamics simulation, e.g., in the framework of the floating frame of reference, a previous model reduction is necessary. A precise representation of the geometry is essential for modeling the dynamics of the impact. However, isoparametric finite elements involve the discretization of the geometry. This work tests isogeometric analysis (IGA) models as an alternative approach in the context of impact simulations in flexible multibody systems. Therefore, the adaption of the flexible multibody system procedure to include IGA models is detailed. The use of nonuniform rational basis splines (NURBS) allows the exact representation of the geometry. The degrees of freedom of the flexible body are afterwards reduced to save computation time in the multibody simulation. To capture precise deformations and stresses in the area of contact as well as elastodynamic effects, a large number of global shape functions is required. As test examples, the impact of an elastic sphere on a rigid surface and the impact of a long elastic rod are simulated and compared to reference solutions.Nonsmooth spatial frictional contact dynamics of multibody systemshttps://www.zbmath.org/1483.700282022-05-16T20:40:13.078697Z"Wang, Kun"https://www.zbmath.org/authors/?q=ai:wang.kun"Tian, Qiang"https://www.zbmath.org/authors/?q=ai:tian.qiang"Hu, Haiyan"https://www.zbmath.org/authors/?q=ai:hu.haiyanSummary: Nonsmooth dynamics algorithms have been widely used to solve the problems of frictional contact dynamics of multibody systems. The linear complementary problems (LCP) based algorithms have been proved to be very effective for the planar problems of frictional contact dynamics. For the spatial problems of frictional contact dynamics, however, the nonlinear complementary problems (NCP) based algorithms usually achieve more accurate results even though the LCP based algorithms can evaluate the friction force and the relative tangential velocity approximately. In this paper, a new computation methodology is proposed to simulate the nonsmooth spatial frictional contact dynamics of multibody systems. Without approximating the friction cone, the cone complementary problems (CCP) theory is used to describe the spatial frictional continuous contact problems such that the spatial friction force can be evaluated accurately. A prediction term is introduced to make the established CCP model be applicable to the cases at high sliding speed. To improve the convergence rate of Newton iterations, the velocity variation of the nonsmooth dynamics equations is decomposed into the smooth velocities and nonsmooth (jump) velocities. The smooth velocities are computed by using the generalized-\(\mathbf{a}\) algorithm, and the nonsmooth velocities are integrated via the implicit Euler algorithm. The accelerated projected gradient descend (APGD) algorithm is used to solve the CCP. Finally, four numerical examples are given to validate the proposed computation methodology.Numerical methods of closed-loop multibody systems with singular configurations based on the geometrical structure of constraintshttps://www.zbmath.org/1483.700292022-05-16T20:40:13.078697Z"Zhuo, Yingpeng"https://www.zbmath.org/authors/?q=ai:zhuo.yingpeng"Qi, Zhaohui"https://www.zbmath.org/authors/?q=ai:qi.zhaohui"Wang, Gang"https://www.zbmath.org/authors/?q=ai:wang.gang.4|wang.gang.5|wang.gang|wang.gang.3|wang.gang.2|wang.gang.1"Guo, Shudong"https://www.zbmath.org/authors/?q=ai:guo.shudongSummary: The geometrical structure of constraints leads to the important conclusion that components of velocities and accelerations in the normal space of the constraint hypersurface are totally determined by the constraints. Orthogonal base vectors of the constraint's normal and tangent spaces can be obtained by the QR decomposition with column permutation. A numerical method of closed-loop multibody systems with singular configurations is presented, in which the traditional hypothesis on independence of constraints is abandoned. Instead of correcting constraint violations at the end of each integration step, positions and velocities are modified to satisfy their constraint equations before they are used to form equations of motion. Such an approach can collaborate with any standard ODE solver. In order to systematically generate constraint equations and obtain the corresponding joint's reaction forces, rotational and translational constraints of a closed-loop are standardized as part of six explicit equations, and a clear relationship between Lagrange multipliers and joint's reaction forces is derived based on the principle of virtual power equivalence. The proposed method can dynamically identify independent constraints and modify the equations of motion accordingly. The numerical examples validated its effectiveness.A collision control strategy for detumbling a non-cooperative spacecraft by a robotic armhttps://www.zbmath.org/1483.700302022-05-16T20:40:13.078697Z"Liu, Xiao-Feng"https://www.zbmath.org/authors/?q=ai:liu.xiaofeng"Zhang, Xiao-Yu"https://www.zbmath.org/authors/?q=ai:zhang.xiaoyu"Cai, Guo-Ping"https://www.zbmath.org/authors/?q=ai:cai.guoping"Wang, Ming-Ming"https://www.zbmath.org/authors/?q=ai:wang.mingmingSummary: Using a space robot to capture a non-cooperative spacecraft with high-speed rotation is significantly challenging since any collision generated during capturing will have great impact on both. To reduce the risk in capturing operations, it is crucial to slow down the rotation velocity of the target before capturing. Hence, this paper studies a collision control strategy for using a robotic arm to detumble a non-cooperative spacecraft. The goal of this strategy is to maintain contact between the robot and the target and to apply continuous detumbling force on the target to slow down its rotational motion. To achieve that, first the mechanism analysis of the two balls for a central collision scenario is performed. Then an overdamping control method is proposed to avoid the separation of the balls after the central collision based on the overdamping property of the mass-spring-damper system, the effectiveness of which is validated theoretically. Finally, to use this overdamping control method in the detumbling missions of space robots, a position-based overdamping control strategy is introduced. In this strategy, the relative dynamic behavior between the robotic arm tip and the contact surface of the target during detumbling is approximated to that of a mass-spring-damper system. Owing to the proposed overdamping control method, the contact between the robot and the target can be maintained, and the space robot can apply continuous control torque to slow down the rotational velocity of the target. Numerical simulations are performed to demonstrate the validity of the proposed control strategy.Inverse dynamics of underactuated planar manipulators without inertial coupling singularitieshttps://www.zbmath.org/1483.700312022-05-16T20:40:13.078697Z"Tafrishi, Seyed Amir"https://www.zbmath.org/authors/?q=ai:tafrishi.seyed-amir"Svinin, Mikhail"https://www.zbmath.org/authors/?q=ai:svinin.mikhail-m"Yamamoto, Motoji"https://www.zbmath.org/authors/?q=ai:yamamoto.motojiSummary: In this paper, we present a model for the inverse dynamics of underactuated manipulators that is free from inertial coupling singularities. The framework's main idea is to include a small-amplitude wave on the trajectory of the rotating active joints. First, we derive the modified nonlinear dynamics for the multijoint manipulators with multiple degrees-of-freedom (DoF). Next, a 4-DoF mass-rotating underactuated manipulator with two passive and two active joints is chosen. Then, a condition assuming the positive definiteness of the inertia matrix is developed to have the singularity-free inverse dynamics. Finally, we analytically study how singularities can be avoided and show an example simulation with a feed-forward control at the singular configuration.Basins of convergence of equilibrium points in the restricted three-body problem with modified gravitational potentialhttps://www.zbmath.org/1483.700322022-05-16T20:40:13.078697Z"Zotos, Euaggelos E."https://www.zbmath.org/authors/?q=ai:zotos.euaggelos-e"Chen, Wei"https://www.zbmath.org/authors/?q=ai:chen.wei.1|chen.wei.2|chen.wei.4|chen.wei|chen.wei.3"Abouelmagd, Elbaz I."https://www.zbmath.org/authors/?q=ai:abouelmagd.elbaz-i"Han, Huiting"https://www.zbmath.org/authors/?q=ai:han.huitingSummary: This article aims to investigate the points of equilibrium and the associated convergence basins in the restricted problem with two primaries, with a modified gravitational potential. In particular, for one of the primary bodies, we add an external gravitational term of the form \(1/r^3\), which is very common in general relativity and represents a gravitational field much stronger than the classical Newtonian one. Using the well-known Newton-Raphson iterator we numerically locate the position of the points of equilibrium, while we also obtain their linear stability. Furthermore, for the location of the points of equilibrium, we obtain semi-analytical functions of both the mass parameter and the transition parameter. Finally, we demonstrate how these two variable parameters affect the convergence dynamics of the system as well as the fractal degree of the basin diagrams. The fractal degree is derived by computing the (boundary) basin entropy.The spatial Hill four-body problem. I: An exploration of basic invariant setshttps://www.zbmath.org/1483.700332022-05-16T20:40:13.078697Z"Burgos-García, Jaime"https://www.zbmath.org/authors/?q=ai:burgos-garcia.jaime"Bengochea, Abimael"https://www.zbmath.org/authors/?q=ai:bengochea.abimael"Franco-Pérez, Luis"https://www.zbmath.org/authors/?q=ai:franco-perez.luisSummary: In this work we perform a first study of basic invariant sets of the spatial Hill's four-body problem, where we have used both analytical and numerical approaches. This system depends on a mass parameter \(\mu\) in such a way that the classical Hill's problem is recovered when \(\mu=0\). Regarding the numerical work, we perform a numerical continuation, for the Jacobi constant \(C\) and several values of the mass parameter \(\mu\) by applying a classical predictor-corrector method, together with a high-order Taylor method considering variable step and order and automatic differentiation techniques, to specific boundary value problems related with the reversing symmetries of the system. The solution of these boundary value problems defines initial conditions of symmetric periodic orbits. Some of the results were obtained departing from periodic orbits within Hill's three-body problem. The numerical explorations reveal that a second distant disturbing body has a relevant effect on the stability of the orbits and bifurcations among these families. We have also found some new families of periodic orbits that do not exist in the classical Hill's three-body problem; these families have some desirable properties from a practical point of view.On the spatial collinear restricted four-body problem with non-spherical primarieshttps://www.zbmath.org/1483.700342022-05-16T20:40:13.078697Z"Suraj, Md Sanam"https://www.zbmath.org/authors/?q=ai:suraj.md-sanam"Aggarwal, Rajiv"https://www.zbmath.org/authors/?q=ai:aggarwal.rajiv"Mittal, Amit"https://www.zbmath.org/authors/?q=ai:mittal.amit"Meena, Om Prakash"https://www.zbmath.org/authors/?q=ai:meena.om-prakash"Asique, Md Chand"https://www.zbmath.org/authors/?q=ai:asique.md-chandSummary: In the present work a systematic study has been presented in the context of the existence of libration points, their linear stability, the regions of motion where the test particle can orbit and the domain of basins of convergence linked to libration points in the spatial configuration of the collinear restricted four-body problem with non-spherical primaries (i.e., the primaries are oblate or prolate spheroid). The parametric evolution of the positions of the libration points as function of the oblateness or prolateness parameters of the primaries and the stability of these points in linear sense are illustrated numerically. Moreover, the numerical investigation shows that the only libration points which lie on either of the axes are linearly stable for several combinations of the oblateness parameter and mass parameter whereas the non-collinear libration points are found linearly unstable, consequently unstable in nonlinear sense also, for studied value of mass parameter and oblateness/prolateness parameter. Moreover, the regions of possible motion are also depicted, where the infinitesimal mass is free to orbit, as function of Jacobian constant. In addition, the basins of convergence (BoC) linked to the libration points are illustrated by using the multivariate version of the Newton-Raphson (NR) iterative scheme.An alternative method to construct a consistent second-order theory on the equilibrium figures of rotating celestial bodieshttps://www.zbmath.org/1483.700352022-05-16T20:40:13.078697Z"López Ortí, José A."https://www.zbmath.org/authors/?q=ai:lopez-orti.jose-antonio"Forner Gumbau, Manuel"https://www.zbmath.org/authors/?q=ai:gumbau.manuel-forner"Barreda Rochera, Miguel"https://www.zbmath.org/authors/?q=ai:rochera.miguel-barredaSummary: The main objective of this work is to construct a new method to develop a consistent second-order amplitudes theory to evaluate the potential of a rotating deformable celestial body when the hydrostatic system equilibrium has been achieved. In this case, we have: \( \vec{\nabla} P = \rho \vec{\nabla} \Psi\), \(\triangle \Psi = - 4 \pi G \rho + 2 \omega^2\), where \(P\) is the pressure, \( \rho\) is the density, \( \Psi\) is the total potential, \( \triangle\) is \textit{Laplace} operator, \(G\) is the gravitational constant and \(\vec{\omega}\) is the angular velocity of the system. To integrate these equations in a general case of mass distribution a state equation relating pressure and density is needed. To assess the full potential, \( \Psi \), it is necessary to calculate the self-gravitational potential, \( \Omega \), and the centrifugal potential, \( V_c\). The equilibrium configuration involves the hydrostatic equilibrium, it is, the rigid rotation of the system corresponding to the minimum potential and, according to Kopal, this state involves the identification of equipotential, isobaric, isothermal and isopycnic surfaces. To study the structure of the body we define a coordinate system \(O X Y Z\) where \(O\) is the center of mass of the component, \( O X\) is an axis fixed in an arbitrary point of the body equator, \( O Z\) an axis parallel to angular velocity \(\overrightarrow{\omega}\) and \(O Y\) defining a direct trihedron. For an arbitrary point \(P\) in the rotating body the Clairaut coordinates are given by \(( a , \theta , \lambda )\) where \(a\) is the radius of the sphere that contains the same mass that the equipotential surface that contains \(P\) and \(( \theta , \lambda )\) are the angular spherical coordinates of \(P\). This problem has been solved in the first order in \(\omega^2\) following two techniques: the first one is based on the asymptotic properties of the numerical quadrature formulae. The second is similar to the one used by Laplace to develop the inverse of the distance between two planets. The second-order theory based on the first method has been developed by the authors in a recent paper. In this work we develop a consistent second-order theory about the equilibrium figures of rotating celestial bodies based on the second method. Finally, to show the performance of the method it is interesting to study a numerical example based on a convective star.A Lie group variational integration approach to the full discretization of a constrained geometrically exact Cosserat beam modelhttps://www.zbmath.org/1483.700362022-05-16T20:40:13.078697Z"Hante, Stefan"https://www.zbmath.org/authors/?q=ai:hante.stefan"Tumiotto, Denise"https://www.zbmath.org/authors/?q=ai:tumiotto.denise"Arnold, Martin"https://www.zbmath.org/authors/?q=ai:arnold.martinSummary: In this paper, we will consider a geometrically exact Cosserat beam model taking into account the industrial challenges. The beam is represented by a framed curve, which we parametrize in the configuration space \(\mathbb{S}^3\ltimes \mathbb{R}^3\) with semi-direct product Lie group structure, where \(\mathbb{S}^3\) is the set of unit quaternions. Velocities and angular velocities with respect to the body-fixed frame are given as the velocity vector of the configuration. We introduce internal constraints, where the rigid cross sections have to remain perpendicular to the center line to reduce the full Cosserat beam model to a Kirchhoff beam model. We derive the equations of motion by Hamilton's principle with an augmented Lagrangian. In order to fully discretize the beam model in space and time, we only consider piecewise interpolated configurations in the variational principle. This leads, after approximating the action integral with second order, to the discrete equations of motion. Here, it is notable that we allow the Lagrange multipliers to be discontinuous in time in order to respect the derivatives of the constraint equations, also known as hidden constraints. In the last part, we will test our numerical scheme on two benchmark problems that show that there is no shear locking observable in the discretized beam model and that the errors are observed to decrease with second order with the spatial step size and the time step size.Kowalewski top and complex Lie algebrashttps://www.zbmath.org/1483.700372022-05-16T20:40:13.078697Z"Jurdjevic, V."https://www.zbmath.org/authors/?q=ai:jurdjevic.velimirSummary: This paper identifies a natural Hamiltonian on a ten dimensional complex Lie algebra that unravels the mysteries encountered in Kowalewski's famous paper on the motions of a rigid body around its fixed point under the influence of gravity. This system reveals that the enigmatic conditions of Kowalewski, namely, two principal moments of inertia equal to each other and twice the value of the remaining moment of inertia, and the centre of gravity in the plane spanned by the directions corresponding to the equal moments of inertia, are both necessary and sufficient for the existence of an isospectral representation \(\frac{dL(\lambda)}{dt}=[M(\lambda), L(\lambda)]\) with a spectral parameter \(\lambda \). This representation then yields a crucial spectral invariant that naturally accounts for all the integrals of motion, known as Kowalewski type integrals in the literature of the top. This result is fundamentally dependent on a preliminary discovery that the equality of two principal moments of inertia and the placement of the centre of mass in the plane spanned by the corresponding directions is intimately tied to the existence of another integral of motion on whose zero level surface the above spectral representation resides. The link between mechanical tops and Hamiltonian systems on Lie algebras is provided by an earlier result in which it is shown that the equations of mechanical tops with a linear potential, (heavy tops, in particular) can be represented on certain coadjoint orbits in the semi-direct product \(\mathfrak{g}=\mathfrak{p}\rtimes\mathfrak{k}\) induced by a closed subgroup \(K\) of the underlying group \(G\). The passage to complex Lie algebras is motivated by Kowalewski's mysterious use of complex variables. It is shown that the complex variables in her paper are naturally identified with complex quaternions and the representation of \(\mathfrak{so}(4,\mathbb{C})\) as the product \(\mathfrak{sl}(2,\mathbb{C})\times \mathfrak{sl}(2,\mathbb{C})\). The paper also shows that all the equations of Kowalewski type can be solved by a uniform integration procedure over the Jacobian of a hyperelliptic curve, as in the original paper of Kowalewski.Non-commutative integrability, exact solvability and the Hamilton-Jacobi theoryhttps://www.zbmath.org/1483.700382022-05-16T20:40:13.078697Z"Grillo, Sergio"https://www.zbmath.org/authors/?q=ai:grillo.sergio-danielFor a given Hamiltonian system, the simplest property that ensures the exact solvability of their corresponding equations of motion is given by the commutative-integrability property, which means that a complete system of known independent first integrals Poisson commute. When such a system, of first integrals, do not commute, one have to use the non-commutative integrability property (NCI). This property requires two extra-conditions: \textit{the isotropy condition} regarding the rank of the matrix formed with the Poisson brackets and \textit{the closure condition} with respect to the Poisson brackets. In this paper, the author constructs two methods that allow to integrate the equation of motion for a given Hamiltonian system from a known set of isotropic first integrals, without using the closure condition.
Reviewer: Ioan Bucataru (Iaşi)Lie symmetry and invariants for a generalized Birkhoffian system on time scaleshttps://www.zbmath.org/1483.700392022-05-16T20:40:13.078697Z"Zhang, Yi"https://www.zbmath.org/authors/?q=ai:zhang.yi.2|zhang.yi.12|zhang.yi.14|zhang.yi.5|zhang.yi.8|zhang.yi.3|zhang.yi.10|zhang.yi.4|zhang.yi.1|zhang.yi.6|zhang.yiSummary: The Lie symmetry and invariants for a generalized Birkhoffian system on time scales are studied, which include exact invariants and adiabatic invariants. First, the generalized Pfaff-Birkhoff principle on time scales is established, and by using Dubois-Reymond lemma the generalized Birkhoff's equations on time scale are derived. Secondly, the determining equations of Lie symmetry for the generalized Birkhoffian system on time scales are established. We prove that if the Lie symmetry satisfies the structural equation, it leads to a conserved quantity, which is an exact invariant of the system. Again, the perturbation of Lie symmetry under the action of small disturbance is considered, the determining equations and the structural equations of disturbed system are established, and the adiabatic invariants led by the Lie symmetry perturbation for the generalized Birkhoffian system on time scales are given. Because of the arbitrariness of selecting time scales and the generality of the generalized Birkhoffian system, the results of this paper are of universal significance. The results of this paper contain the corresponding results for Birkhoffian system on time scales and classical generalized Birkhoffian system as its special cases. At the end of the paper, an example is given to illustrate the validity of the method and the results.Fractional-order modeling and nonlinear dynamic analyses of the rotor-bearing-seal systemhttps://www.zbmath.org/1483.700402022-05-16T20:40:13.078697Z"Yan, Donglin"https://www.zbmath.org/authors/?q=ai:yan.donglin"Wang, Weiyu"https://www.zbmath.org/authors/?q=ai:wang.weiyu"Chen, Qijuan"https://www.zbmath.org/authors/?q=ai:chen.qijuanSummary: Unexpected vibrations induced by sealing and bearing faults in the rotor-bearing-seal system seriously affect the health and reliability of the rotating machinery. Here, to study the vibration performances more accurately, the sealing force model is extended from a very narrow integer-order scope to a flexible fractional-order scope, and a novel fractional-order mathematical model of the rotor-bearing-seal system is established from the view of engineering applications by using the finite element method. As a pioneering work, the effect of the fractional order of sealing on the journal and rotor are analyzed under different rotational speeds. Besides, the dynamic characteristics of the rotor-bearing-seal system with the changing rotational speed, mass eccentricity of rotor, sealing clearance and sealing pressure drop at a specific fractional order of sealing are also studied in detail. Then some stability discussions of the system are presented, which is synchronous with some special frequency characteristics. Finally, the methods and results can efficiently provide a theoretical reference for the design and operation of the rotor-bearing-seal system and be applied to forecasting and diagnosing vibration faults of them.Jacobi stability analysis and the onset of chaos in a two-degree-of-freedom mechanical systemhttps://www.zbmath.org/1483.700412022-05-16T20:40:13.078697Z"Wang, Fanrui"https://www.zbmath.org/authors/?q=ai:wang.fanrui"Liu, Ting"https://www.zbmath.org/authors/?q=ai:liu.ting"Kuznetsov, Nikolay V."https://www.zbmath.org/authors/?q=ai:kuznetsov.nikolay-v"Wei, Zhouchao"https://www.zbmath.org/authors/?q=ai:wei.zhouchaoParametric vibrational resonance in a gyroscope driven by dual-frequency forceshttps://www.zbmath.org/1483.700422022-05-16T20:40:13.078697Z"Oyeleke, K. S."https://www.zbmath.org/authors/?q=ai:oyeleke.k-s"Olusola, O. I."https://www.zbmath.org/authors/?q=ai:olusola.olasunkanmi-i"Vincent, U. E."https://www.zbmath.org/authors/?q=ai:vincent.uchechukwu-e"Ghosh, D."https://www.zbmath.org/authors/?q=ai:ghosh.debkumar|ghosh.d-p|ghosh.dipak.1|ghosh.dibyendu|ghosh.dilip-kumar.1|ghosh.dipankar.1|ghosh.damayanti|ghosh.debashis|ghosh.debashis.1|ghosh.d-t|ghosh.debdulal|ghosh.dipanwita|ghosh.debabrata.1|ghosh.debi-prasad|ghosh.dilip-kumar|ghosh.dipak|ghosh.debraj|ghosh.debidas|ghosh.deb|ghosh.dibakar|ghosh.deb-kumar|ghosh.debjit|ghosh.debarati|ghosh.debarghya|ghosh.debarun|ghosh.dalim-k|ghosh.diptesh|ghosh.debashri|ghosh.debodirna|ghosh.debasis|ghosh.debdas|ghosh.dona|ghosh.debabrata-kumar|ghosh.debayani|ghosh.debabrata.2|ghosh.dhrubajyoti|ghosh.debojyoti|ghosh.diptimoy|ghosh.diptabibhu|ghosh.deep"McClintock, P. V. E."https://www.zbmath.org/authors/?q=ai:mcclintock.peter-vaughan-elsmereSummary: We examine and analyze vibrational resonance (VR) in a dual-frequency-driven gyroscope subject to a parametric excitation and an additive periodic forces. The method of direct separation of the fast and slow motions is used to derive the response amplitude analytically from the equation for slow oscillations of the system, in terms of the parameters of the high-frequency signal and the parametric excitation. Numerical simulations are carried out to validate the theoretical results. It is further shown that, when the parametric excitation and additive periodic force consist of low and high frequencies, respectively, a much higher response amplitude can occur. It is about three times larger than the response obtained when the forcing actions are reversed and is attributable to the optimization of low-frequency parametric excitation by the high-frequency additive signal.Schemes of momentum/reaction wheels unloading by mechanical restructuring and gearbox for spacecrafthttps://www.zbmath.org/1483.700432022-05-16T20:40:13.078697Z"Doroshin, Anton V."https://www.zbmath.org/authors/?q=ai:doroshin.anton-vSummary: A new principle and linked schemes of reaction/momentum wheels unloading are proposed and constructed. This principle is based on the instantaneous restructuring and changing the mechanical system itself, when additional internal degrees of freedom become available. These releasing additional degrees of freedom correspond to additional rotors, which take ``after unfreezing'' their own opportunity to rotate. At the connection of additional ``unfrozen'' rotors to the main wheels by gear type, these rotors become involved in the rotation with opposite direction relatively to the main wheels rotation, and it instantaneously provides nulling the relative angular momentum. Then electric motors of additional rotors and wheels can start the process of the rotational energy recovery, which decelerates and unloads angular velocities of all rotors and wheels. The proposed principle of releasing additional degrees of freedom and reconfiguring internal mechanical multi-rotor subsystem allow to immediately change values and directions of the relative angular momentum. This changeable multi-rotor subsystem represents the multifunctional attitude control system, which can be figuratively called as a ``gearbox''. As a part of the gearbox a special mechanical device is proposed, which represents a ``gravitational damper'' to unloading the total absolute angular momentum of spacecraft with the help of external gravitational torques.Analysis of driving styles of a GP2 car via minimum lap-time direct trajectory optimizationhttps://www.zbmath.org/1483.700442022-05-16T20:40:13.078697Z"Gabiccini, M."https://www.zbmath.org/authors/?q=ai:gabiccini.marco"Bartali, L."https://www.zbmath.org/authors/?q=ai:bartali.l"Guiggiani, M."https://www.zbmath.org/authors/?q=ai:guiggiani.massimoSummary: This paper addresses the problem of the link between the driving style of an ideal driver, modelled as an optimal controller, and fundamental set-up parameters of a vehicle in the GP2 motorsport class. The aim is to evaluate quantitatively how set-up parameters, like distribution of aerodynamic loads, weight and roll stiffness between front and rear axles, affect the driving style, encoded in the shape of the optimal trajectory and in the acceleration, brake and steer inputs.
To this aim, we develop an optimization code that includes a double-track vehicle model capable of solving the minimum lap-time problem (MLTP) on a given track. The track is represented via NURBS curves and the MLTP is framed and solved as an optimal control problem by transcription into a nonlinear program using direct collocation. To assess the accuracy of the vehicle model and the optimization pipeline, we also validate our results against real telemetry data.
The developed software framework lends itself to easily perform both sensitivity analysis and concurrent trajectory planning and set-up parameter optimization: this is obtained by simple promotion of static parameters of interests to variables in the optimal control problem. Some results along these lines are also included.Research on mechanism and control methods of carbody chattering of an electric multiple-unit trainhttps://www.zbmath.org/1483.700452022-05-16T20:40:13.078697Z"Gong, Dao"https://www.zbmath.org/authors/?q=ai:gong.dao"Liu, Guangyu"https://www.zbmath.org/authors/?q=ai:liu.guangyu"Zhou, Jinsong"https://www.zbmath.org/authors/?q=ai:zhou.jinsongSummary: Carbody chattering is an abnormal vibration that severely deteriorates the ride quality of a railway vehicle. However, systematic studies on the mechanisms and control methods of carbody chattering are inadequate. Hence, in-situ tests, wheel and rail profile tests, modal parameter tests, and root locus analyses were conducted for an electric multiple-unit train to study the carbody chattering mechanism. Results show significant concave wear on wheel treads that have not yet met their wheel-turning mileages. When the vehicle moves from a carbody non-chattering to a chattering section, the wheel-rail contact positions are scattered and jumping is observed; then, the wheel-rail contact conicity increases rapidly, causing the modal damping ratio of the bogie hunting motion to reduce to 0, the bogie to change from stable to critical-unstable state, and bogie hunting motion frequency to increase close to the modal frequency of the carbody diamond-shaped deformation, thereby triggering synchronous movement. This amplifies the modal vibration, causing carbody chattering. Therefore, three control methods are proposed for carbody chattering -- turning worn wheels; grinding rail profiles in the carbody chattering section; and synchronous optimisation of the primary longitudinal and lateral positioning stiffness, node stiffness, and damping coefficient of the yaw damper -- according to the multi-objective synchronisation optimisation method to improve operational stability and ride quality. Test results show that all three methods effectively control carbody chattering; compared to the original vehicle, the amplitude of carbody chattering acceleration at 10 Hz can be reduced by 90\%, 40\% and 60\% for the three methods.Remote trajectory tracking of rigid bodies immersed in a two-dimensional perfect incompressible fluidhttps://www.zbmath.org/1483.760182022-05-16T20:40:13.078697Z"Glass, Olivier"https://www.zbmath.org/authors/?q=ai:glass.olivier"Kolumbán, József J."https://www.zbmath.org/authors/?q=ai:kolumban.jozsef-j"Sueur, Franck"https://www.zbmath.org/authors/?q=ai:sueur.franckSummary: We consider the motion of several rigid bodies immersed in a two-dimensional incompressible perfect fluid, the whole system occupying a bounded simply connected domain. The external fixed boundary is impermeable except on an open nonempty part where one controls both the normal velocity, allowing some fluid to go in and out of the domain, and the entering vorticity. The motion of the rigid bodies is given by the Newton laws with forces due to the fluid pressure and the fluid motion is described by the incompressible Euler equations. We prove that it is possible to exactly achieve any noncolliding smooth motion of the rigid bodies by the remote action of a controlled normal velocity on the outer boundary which takes the form of state-feedback, with zero entering vorticity. The proof relies on a nonlinear method to solve linear perturbations of nonlinear equations associated with a quadratic operator.Heat flux structure for Ornstein-Uhlenbeck particles of a one-dimensional harmonic chainhttps://www.zbmath.org/1483.800032022-05-16T20:40:13.078697Z"Guzev, M. A."https://www.zbmath.org/authors/?q=ai:guzev.mikhail-a|guzev.mickhail-a"Gorbunov, A. V."https://www.zbmath.org/authors/?q=ai:gorbunov.a-vSummary: A one-dimensional harmonic chain of \(N\) particles is considered, located between two thermal reservoirs (Ornstein-Uhlenbeck particles). An exact solution is constructed for the system of equations describing the dynamics of the system. On the basis of this solution, an analytical expression is obtained for the discrete expression of the heat flux of the model under study, when the time \(t \to \infty \), which corresponds to the consideration of stationary transport conditions. It is shown that the heat flux includes two physically different components. The first of them is proportional to the temperature difference between the reservoirs and characterizes the heat transfer along the chain. The second determines the initial value of the flow when the temperatures of the tanks are equal.Entanglement of classical and quantum short-range dynamics in mean-field systemshttps://www.zbmath.org/1483.810272022-05-16T20:40:13.078697Z"Bru, J.-B."https://www.zbmath.org/authors/?q=ai:bru.jean-bernard"de Siqueira Pedra, W."https://www.zbmath.org/authors/?q=ai:pedra.w-de-siqueira|de-siqueira-pedra.walterSummary: The relationship between classical and quantum mechanics is usually understood via the limit \(\hbar\to 0\). This is the underlying idea behind the quantization of classical objects. The apparent incompatibility of general relativity with quantum mechanics and quantum field theory has challenged for many decades this basic idea. We recently showed [the authors, J. Math. Anal. Appl. 493, No. 1, Article ID 124434, 61 p. (2021; Zbl 1451.82023); J. Math. Anal. Appl. 493, No. 1, Article ID 124517, 65 p. (2021; Zbl 1451.82025)] the emergence of classical dynamics for very general quantum lattice systems with mean-field interactions, without (complete) suppression of its quantum features, in the infinite volume limit. This leads to a theoretical framework in which the classical and quantum worlds are entangled. Such an entanglement is noteworthy and is a consequence of the highly non-local character of mean-field interactions. Therefore, this phenomenon should not be restricted to systems with mean-field interactions only, but should also appear in presence of interactions that are sufficiently long-range, yielding effective, classical background fields, in the spirit of the Higgs mechanism of quantum field theory. In order to present the result in a less abstract way than in its original version, here we apply it to a concrete, physically relevant, example and discuss, by this means, various important aspects of our general approach. The model we consider is not exactly solvable and the particular results obtained are new.Statistical complexity of the kicked top model considering chaoshttps://www.zbmath.org/1483.810342022-05-16T20:40:13.078697Z"Fülöp, Ágnes"https://www.zbmath.org/authors/?q=ai:fulop.agnesSummary: The concept of the statistical complexity is studied to characterize the classical kicked top model which plays important role in the qbit systems and the chaotic properties of the entanglement. This allow us to understand this driven dynamical system by the probability distribution in phase space to make distinguish among the regular, random and structural complexity on finite simulation. We present the dependence of the kicked top and kicked rotor model through the strength excitation in the framework of statistical complexity.Shortcut to adiabatic two-qubit state swap in a superconducting circuit QED via effective drivingshttps://www.zbmath.org/1483.810412022-05-16T20:40:13.078697Z"Li, Ming"https://www.zbmath.org/authors/?q=ai:li.ming|li.ming.3|li.ming.1|li.ming.8|li.ming.9|li.ming.2|li.ming.5|li.ming.4|li.ming.6|li.ming.7"Dong, Xin-Ping"https://www.zbmath.org/authors/?q=ai:dong.xin-ping"Yan, Run-Ying"https://www.zbmath.org/authors/?q=ai:yan.run-ying"Lu, Xiao-Jing"https://www.zbmath.org/authors/?q=ai:lu.xiaojing"Zhao, Zheng-Yin"https://www.zbmath.org/authors/?q=ai:zhao.zheng-yin"Feng, Zhi-Bo"https://www.zbmath.org/authors/?q=ai:feng.zhi-boSummary: Optimal two-qubit operation is of significance to quantum information processing. An efficient scheme is proposed for realizing the shortcut to adiabatic two-qubit state swap in a superconducting circuit quantum electrodynamics (QED) via effective drivings. Two superconducting qutrits are coupled to a common cavity field and individual classical drivings. Based on two Gaussian-type Rabi drivings, two-qubit state swap can be adiabatically implemented within a reduced three-state system. To speed up the operation, these two original Rabi drivings are modified in the framework of shortcuts to adiabaticity, instead of adding an extra counterdiabatic driving. Moreover, owing to a shorter duration time, the decoherence effects on the accelerated quantum operation can be mitigated significantly. The strategy could offer an optimized method to construct fast and robust quantum operations on superconducting qubits experimentally.Effective adiabatic control of a decoupled Hamiltonian obtained by rotating wave approximationhttps://www.zbmath.org/1483.810832022-05-16T20:40:13.078697Z"Augier, Nicolas"https://www.zbmath.org/authors/?q=ai:augier.nicolas"Boscain, Ugo"https://www.zbmath.org/authors/?q=ai:boscain.ugo"Sigalotti, Mario"https://www.zbmath.org/authors/?q=ai:sigalotti.marioSummary: In this paper we study up to which extent we can apply adiabatic control strategies to a quantum control model obtained by rotating wave approximation. In particular, we show that, under suitable assumptions on the asymptotic regime between the parameters characterizing the rotating wave and the adiabatic approximations, the induced flow converges to the one obtained by considering the two approximations separately and by combining them formally in cascade. As a consequence, we propose explicit control laws which can be used to induce desired populations transfers, robustly with respect to parameter dispersions in the controlled Hamiltonian.Erratum to: ``Reducible gauge symmetry versus unfree gauge symmetry in Hamiltonian formalism''https://www.zbmath.org/1483.810992022-05-16T20:40:13.078697Z"Abakumova, V. A."https://www.zbmath.org/authors/?q=ai:abakumova.v-a"Karataeva, I. Yu."https://www.zbmath.org/authors/?q=ai:karataeva.i-yu"Lyakhovich, S. L."https://www.zbmath.org/authors/?q=ai:lyakhovich.simon-lCorrects six formulas in the authors' paper [ibid. 973, Article ID 115577, 30 p. (2021; Zbl 1480.81088)].Reformulation of gauge theories in terms of gauge invariant fieldshttps://www.zbmath.org/1483.811012022-05-16T20:40:13.078697Z"Fontana, Pierpaolo"https://www.zbmath.org/authors/?q=ai:fontana.pierpaolo"Pinto Barros, Joao C."https://www.zbmath.org/authors/?q=ai:pinto-barros.joao-c"Trombettoni, Andrea"https://www.zbmath.org/authors/?q=ai:trombettoni.andreaSummary: We present a reformulation of gauge theories in terms of gauge invariant fields. Focusing on abelian theories, we show that the gauge and matter covariant fields can be recombined to introduce new gauge invariant degrees of freedom. Starting from the \((1+1)\) dimensional case on the lattice, with both periodic and open boundary conditions, we then generalize to higher dimensions and to the continuum limit. To show explicit and physically relevant examples of the reformulation, we apply it to the Hamiltonian of a single particle in a (static) magnetic field, to pure abelian lattice gauge theories, to the Lagrangian of quantum electrodynamics in \((3+1)\) dimensions and to the Hamiltonian of the \(2d\) and the \(3d\) Hofstadter model. In the latter, we show that the particular construction used to eliminate the gauge covariant fields enters the definition of the magnetic Brillouin zone. Finally, we briefly comment on relevance of the presented reformulation to the study of interacting gauge theories.Chern-Simons perturbative series revisitedhttps://www.zbmath.org/1483.811082022-05-16T20:40:13.078697Z"Lanina, E."https://www.zbmath.org/authors/?q=ai:lanina.elena|lanina.e-g"Sleptsov, A."https://www.zbmath.org/authors/?q=ai:sleptsov.alexey"Tselousov, N."https://www.zbmath.org/authors/?q=ai:tselousov.nSummary: A group-theoretical structure in a perturbative expansion of the Wilson loops in the 3d Chern-Simons theory with \(SU(N)\) gauge group is studied in symmetric approach. A special basis in the center of the universal enveloping algebra \(ZU(\mathfrak{sl}_N)\) is introduced. This basis allows one to present group factors in an arbitrary irreducible finite-dimensional representation. Developed methods have wide applications, the most straightforward and evident ones are mentioned. Namely, Vassiliev invariants of higher orders are computed, a conjecture about existence of new symmetries of the colored HOMFLY polynomials is stated, and the recently discovered tug-the-hook symmetry of the colored HOMFLY polynomial is proved.Implications for colored HOMFLY polynomials from explicit formulas for group-theoretical structurehttps://www.zbmath.org/1483.811092022-05-16T20:40:13.078697Z"Lanina, E."https://www.zbmath.org/authors/?q=ai:lanina.e-g|lanina.elena"Sleptsov, A."https://www.zbmath.org/authors/?q=ai:sleptsov.alexey"Tselousov, N."https://www.zbmath.org/authors/?q=ai:tselousov.nSummary: We have recently proposed [Phys. Lett., B 823, Article ID 136727, 8 p. (2021; Zbl 1483.81108)] a powerful method for computing group factors of the perturbative series expansion of the Wilson loop in the Chern-Simons theory with \(SU(N)\) gauge group. In this paper, we apply the developed method to obtain and study various properties, including nonperturbative ones, of such vacuum expectation values.
First, we discuss the computation of Vassiliev invariants. Second, we discuss the Vogel theorem of not distinguishing chord diagrams by weight systems coming from semisimple Lie (super)algebras. Third, we provide a method for constructing linear recursive relations for the colored Jones polynomials considering a special case of torus knots \(T[2, 2 k + 1]\). Fourth, we give a generalization of the one-hook scaling property for the colored Alexander polynomials. And finally, for the group factors we provide a combinatorial description, which has a clear dependence on the rank \(N\) and the representation \(R\).D-brane description from nontrivial M2-braneshttps://www.zbmath.org/1483.811182022-05-16T20:40:13.078697Z"Garcia del Moral, M. P."https://www.zbmath.org/authors/?q=ai:garcia-del-moral.maria-pilar"Las Heras, C."https://www.zbmath.org/authors/?q=ai:las-heras.cSummary: We obtain the bosonic D-brane description of toroidally compactified non-trivial M2-branes with the unique property of having a purely discrete supersymmetric regularized spectrum with finite multiplicity. As a byproduct, we generalize the previous Hamiltonian formulation to describe a M2-brane on a completely general constant quantized background \(C_3\) denoted by us as CM2-brane. We show that under this condition, the theory is equivalent to a more restricted one, denoted as an M2-brane with \(C_\pm\) fluxes, which has been shown to have good quantum behavior. As a result, the spectral properties of both sectors must be the same. We then obtain its bosonic D-brane description and discover new symmetries. We find that it contains a new symplectic gauge field in addition to the expected U(1) Dirac-Born-Infeld gauge symmetry and a nontrivial \(U(1)\) associated with the presence of 2-form fluxes. Its bundle description takes on a new structure in the form of a twisted torus bundle. By turning off some of the fields, the D-brane description of other toroidally nontrivial M2-brane sectors can be obtained from this one. The possibility of reinterpreting these sectors in terms of Dp-brane bound states is discussed. These D-brane descriptions constitute String theory sectors with a quantum consistent uplift to M-theory.The Veneziano amplitude via mostly BRST exact operatorhttps://www.zbmath.org/1483.811192022-05-16T20:40:13.078697Z"Kishimoto, Isao"https://www.zbmath.org/authors/?q=ai:kishimoto.isao"Sasaki, Tomoko"https://www.zbmath.org/authors/?q=ai:sasaki.tomoko"Seki, Shigenori"https://www.zbmath.org/authors/?q=ai:seki.shigenori"Takahashi, Tomohiko"https://www.zbmath.org/authors/?q=ai:takahashi.tomohikoSummary: The Veneziano amplitude is derived from fixing one degree of freedom of \(PSL(2, \mathbb{R})\) symmetry by the insertion of a mostly BRST exact operator. Evaluating the five-point function which consists of four open string tachyons and this gauge fixing operator, we find it equals the Veneziano amplitude up to a sign factor. The sign factor is interpreted as a signed intersection number. The result implies that the mostly BRST exact operator, which is originally used to provide two-point string amplitudes, correctly fixes the \(PSL(2, \mathbb{R})\) gauge symmetry for general amplitudes. We conjecture an expression for general \(n\)-point tree amplitudes with an insertion of this gauge fixing operator.Finite-\(N\) corrections to the superconformal index of toric quiver gauge theorieshttps://www.zbmath.org/1483.811232022-05-16T20:40:13.078697Z"Arai, Reona"https://www.zbmath.org/authors/?q=ai:arai.reona"Fujiwara, Shota"https://www.zbmath.org/authors/?q=ai:fujiwara.shota"Imamura, Yosuke"https://www.zbmath.org/authors/?q=ai:imamura.yosuke"Mori, Tatsuya"https://www.zbmath.org/authors/?q=ai:mori.tatsuyaSummary: The superconformal index of quiver gauge theories realized on D3-branes in toric Calabi-Yau cones is investigated. We use the AdS/CFT correspondence and study D3-branes wrapped on supersymmetric cycles. We focus on brane configurations in which a single D3-brane is wrapped on a cycle, and we do not take account of branes with multiple wrapping. We propose a formula that gives finite-\(N\) corrections to the index caused by such brane configurations. We compare the predictions of the formula for several examples with the results on the gauge theory side obtained by using localization for small sizes of gauge groups, and confirm that the formula correctly reproduces the finite-\(N\) corrections up to the expected order.Kink solutions in logarithmic scalar field theory: excitation spectra, scattering, and decay of bionshttps://www.zbmath.org/1483.811252022-05-16T20:40:13.078697Z"Belendryasova, Ekaterina"https://www.zbmath.org/authors/?q=ai:belendryasova.ekaterina"Gani, Vakhid A."https://www.zbmath.org/authors/?q=ai:gani.vakhid-a"Zloshchastiev, Konstantin G."https://www.zbmath.org/authors/?q=ai:zloshchastiev.konstantin-gSummary: We consider the \((1 + 1)\)-dimensional Lorentz-symmetric field-theoretic model with logarithmic potential having a Mexican-hat form with two local minima similar to that of the quartic Higgs potential in conventional electroweak theory with spontaneous symmetry breaking and mass generation. We demonstrate that this model allows topological solutions -- kinks. We analyze the kink excitation spectrum, and show that it does not contain any vibrational modes. We also study the scattering dynamics of kinks for a wide range of initial velocities. The critical value of the initial velocity occurs in kink-antikink collisions, which thus differentiates two regimes. Below this value, we observe the capture of kinks and their fast annihilation; while above this value, the kinks bounce off and escape to spatial infinities. Numerical studies show no resonance phenomena in the kink-antikink scattering.Physics of the inverted harmonic oscillator: From the lowest Landau level to event horizonshttps://www.zbmath.org/1483.811392022-05-16T20:40:13.078697Z"Subramanyan, Varsha"https://www.zbmath.org/authors/?q=ai:subramanyan.varsha"Hegde, Suraj S."https://www.zbmath.org/authors/?q=ai:hegde.suraj-s"Vishveshwara, Smitha"https://www.zbmath.org/authors/?q=ai:vishveshwara.smitha"Bradlyn, Barry"https://www.zbmath.org/authors/?q=ai:bradlyn.barrySummary: In this work, we present the inverted harmonic oscillator (IHO) Hamiltonian as a paradigm to understand the quantum mechanics of scattering and time-decay in a diverse set of physical systems. As one of the generators of area preserving transformations, the IHO Hamiltonian can be studied as a dilatation generator, squeeze generator, a Lorentz boost generator, or a scattering potential. In establishing these different forms, we demonstrate the physics of the IHO that underlies phenomena as disparate as the Hawking-Unruh effect and scattering in the lowest Landau level (LLL) in quantum Hall systems. We derive the emergence of the IHO Hamiltonian in the LLL in a gauge invariant way and show its exact parallels with the Rindler Hamiltonian that describes quantum mechanics near event horizons. This approach of studying distinct physical systems with symmetries described by isomorphic Lie algebras through the emergent IHO Hamiltonian enables us to reinterpret geometric response in the lowest Landau level in terms of relativistic effects such as Wigner rotation. Further, the analytic scattering matrix of the IHO points to the existence of quasinormal modes (QNMs) in the spectrum, which have quantized time-decay rates. We present a way to access these QNMs through wave packet scattering, thus proposing a novel effect in quantum Hall point contact geometries that parallels those found in black holes.Non-conformal attractor in boost-invariant plasmashttps://www.zbmath.org/1483.811432022-05-16T20:40:13.078697Z"Chattopadhyay, Chandrodoy"https://www.zbmath.org/authors/?q=ai:chattopadhyay.chandrodoy"Jaiswal, Sunil"https://www.zbmath.org/authors/?q=ai:jaiswal.sunil-prasad"Du, Lipei"https://www.zbmath.org/authors/?q=ai:du.lipei"Heinz, Ulrich"https://www.zbmath.org/authors/?q=ai:heinz.ulrich"Pal, Subrata"https://www.zbmath.org/authors/?q=ai:pal.subrataSummary: We study the dissipative evolution of (0+1)-dimensionally expanding media with Bjorken symmetry using the Boltzmann equation for massive particles in relaxation-time approximation. Breaking conformal symmetry by a mass induces a non-zero bulk viscous pressure in the medium. It is shown that even a small mass (in units of the local temperature) drastically modifies the well-known attractor for the shear Reynolds number previously observed in massless systems. For generic nonzero particle mass, neither the shear nor the bulk viscous pressure relax quickly to a non-equilibrium attractor; they approach the hydrodynamic limit only late, at small values of the inverse Reynolds numbers.
Only the longitudinal pressure, which is a combination of thermal, shear and bulk viscous pressures, continues to show early approach to a far-off-equilibrium attractor, driven by the rapid longitudinal expansion at early times. Second-order dissipative hydrodynamics based on a gradient expansion around locally isotropic thermal equilibrium fails to reproduce this attractor.Center group dominance in quark confinementhttps://www.zbmath.org/1483.811472022-05-16T20:40:13.078697Z"Ikeda, Ryu"https://www.zbmath.org/authors/?q=ai:ikeda.ryu"Kondo, Kei-Ichi"https://www.zbmath.org/authors/?q=ai:kondo.kei-ichiSummary: We show that the color \(N\)-dependent area law falloffs of the double-winding Wilson loop averages for the \(SU(N)\) lattice gauge theory obtained in previous works are reproduced from the corresponding lattice abelian gauge theory with the center gauge group \(Z_N\). This result indicates the center group dominance in quark confinement.The Polyakov loop dependence of bulk viscosity of QCD matterhttps://www.zbmath.org/1483.811492022-05-16T20:40:13.078697Z"Mukhopadhay, Debmalya"https://www.zbmath.org/authors/?q=ai:mukhopadhay.debmalya"Alam, Jan-e"https://www.zbmath.org/authors/?q=ai:alam.jan-e"Kumar, R."https://www.zbmath.org/authors/?q=ai:kumar.ravinder.6|kumar.rakesh.6|kumar.ravinder.4|kumar.rakesh.4|kumar.r-sunil|kumar.ratnesh-r|kumar.rohit|kumar.rajnish|kumar.renjith-r|kumar.ranjan|kumar.ramnivas|kumar.r-vijay|kumar.r-anantha|kumar.roushan|kumar.ram-l|kumar.r-naveen|kumar.rajnesh|kumar.ronald-ravinesh|kumar.rahuthanahalli-thimmegowda-naveen|kumar.rajan|kumar.raman|kumar.rajive|kumari.rachna|kumar.rupesh|kumar.rajeeva|kumar.rajnish.1|kumar.r-v-m-s-s-kiran|kumar.raj|kumar.rahul|kumar.ranjeth|kumar.r-vinodh|kumar.romesh|kumar.raju|kumar.ravi-shankar|kumar.rathish-b-v|kumar.ranjit|kumar.ram-awadhesh|kumar.r-david|kumar.r-ram|kumar.r-sukesh|kumar.rajinder|kumar.rajiv|kumar.r-kishore|kumar.r-krishna|kumar.ravendra|kumar.rajagounder-ravi|kumar.ritesh|kumar.ranjeet|kumar.rajnessh|kumar.ramayya|kumar.raushan|kumar.r-praveen|kumar.ranbir|kumar.r-pradeep|kumar.r-v-raja|kumar.ramana|kumar.rachitesh|kumar.rajeev|kumar.r-ramesh|kumar.r-arun|kumar.ravi-k|kumar.rajendar|kumar.ranganathan|kumar.r-harish|kumar.rajender|kumar.raghvendra|kumar.rohini|kumar.ravindra|kumar.revant|kumar.r-g|kumar.rukmini|kumar.rishi|kumar.rohtash|kumar.r-suresh|kumar.ronit|kumar.r-selva|kumar.rajendra|kumar.ramesh-c|kumar.rajneesh|kumar.ranjitha|kumar.ripendra|kumar.reddi-kiran|kumar.rajesh-s|kumar.ramanjit|kumar.raghu|kumar.r-vimalSummary: In this work, we show the dependence of bulk viscosity on Polyakov loop in 3+1 dimensional topologically massive model (TMM). This model contains equally massive non-Abelian gauge fields without spontaneous symmetry breaking. In earlier works, the bulk viscosity was found from the trace anomaly in massless \(\phi^4\) model and Yang-Mills (YM) theory and its dependence on the quantum corrections was established. In TMM, the trace anomaly is absent due to the presence of kinetic term of a two-form field \(B\) in the action. This model also provides the dependence of bulk viscosity on the mass of the gauge bosons. The mass of the gauge bosons in TMM acts as magnetic mass in the perturbative thermal field theory. This magnetic mass is gauge independent unlike what is found in massless YM theory. We also observe that the strong coupling constant has the same behaviour at high energy limit (i.e. asymptotic freedom) as that of massless YM theory at zero temperature.Formulation of a shell-cluster overlap integral with the Gaussian expansion methodhttps://www.zbmath.org/1483.811602022-05-16T20:40:13.078697Z"Nakamoto, R."https://www.zbmath.org/authors/?q=ai:nakamoto.ritsuo"Ueda, E."https://www.zbmath.org/authors/?q=ai:ueda.eiichiro|ueda.etsuyo"Ito, M."https://www.zbmath.org/authors/?q=ai:ito.masatoshi"Shimizu, N."https://www.zbmath.org/authors/?q=ai:shimizu.nobutaka|shimizu.nobuyuki|shimizu.noritaka|shimizu.nobukiSummary: We formulate a computational method to evaluate the overlap integral of the shell-model and cluster-model wave functions. The framework is applied to the system of the core plus two neutrons, and the magnitude of the overlap of the shell-model configuration (core + \(n + n\)) and the di-neutron cluster one (core + \(2n\)) is explored. We have found that the magnitude of the overlap integral is prominently enhanced when two neutrons occupy shell-model orbits with low orbital angular momenta, such as \(s\)- and \(p\)-wave orbits. The shell-cluster overlap is calculated in systems with \(jj\)-closed cores plus two neutrons, and the enhancement due to occupation of the \(s\) or \(p\) orbit also occurs in the systematic calculation. The effect of the configuration interaction on the shell-cluster overlap integrals is also discussed.Co-spherical electronic configuration of the helium-like atomic systemshttps://www.zbmath.org/1483.811622022-05-16T20:40:13.078697Z"Liverts, Evgeny Z."https://www.zbmath.org/authors/?q=ai:liverts.evgeny-zSummary: The properties of a special configuration of a helium-like atomic system, when both electrons are on the surface of a sphere of radius \(r\), and angle \(\theta\) characterizes their positions on sphere, are investigated. Unlike the previous studies, \(r\) is considered as a quantum mechanical variable but not a parameter. It is important that the ``co-spherical'' and the ``collinear'' configuration are coincident in two points. For \(\theta=0\) one obtains the state of the electron-electron coalescence, whereas the angle \(\theta=\pi\) characterizes the \textbf{e-n-e} configuration when the electrons are located at the ends of the diameter of sphere with the nucleus at its center. The Pekeris-like method representing a fully three-body variational technique is used for the expedient calculations. Some interesting features of the expectation values representing the basic characteristics of the ``co-spherical'' electronic configuration are studied. The unusual properties of the expectation values of the operators associated with the kinetic and potential energy of the two-electron atom/ion possessing the ``co-spherical'' configuration are found. Refined formulas for calculations of the two-electron Fock expansion by the Green's function approach are presented. The model wave functions of high accuracy describing the ``co-spherical'' electronic configuration are obtained. All results are illustrated in tables and figures.Three-boson stability for boosted interactions towards the zero-range limithttps://www.zbmath.org/1483.811712022-05-16T20:40:13.078697Z"Mohseni, K."https://www.zbmath.org/authors/?q=ai:mohseni.kamran"Chaves, A. J."https://www.zbmath.org/authors/?q=ai:chaves.a-j"da Costa, D. R."https://www.zbmath.org/authors/?q=ai:da-costa.diogo-ricardo"Frederico, T."https://www.zbmath.org/authors/?q=ai:frederico.tobias"Hadizadeh, M. R."https://www.zbmath.org/authors/?q=ai:hadizadeh.mohammad-rezaSummary: We study the three-boson bound-state mass and wave functions for ground and excited states within the three-body relativistic framework with Kamada and Glöcke boosted potentials in the limit of a zero-range interaction. We adopt a nonrelativistic short-range separable potential, with Yamaguchi and Gaussian form factors, and drive them towards the zero-range limit by letting the form factors' momentum scales go to large values while keeping the two-body binding fixed. We show that the three-boson relativistic masses and wave functions are model-independent towards the zero-range limit, and the Thomas collapse is avoided, while the nonrelativistic limit kept the Efimov effect. Furthermore, the stability in the zero-range limit is a result of the reduction of boosted potential with the increase of the virtual pair center of mass momentum within the three-boson system. Finally, we compare the present results with Light-Front and Euclidean calculations.Modeling of compact stars: an anisotropic approachhttps://www.zbmath.org/1483.830042022-05-16T20:40:13.078697Z"Das, Shyam"https://www.zbmath.org/authors/?q=ai:das.shyam"Singh, Ksh. Newton"https://www.zbmath.org/authors/?q=ai:singh.ksh-newton"Baskey, Lipi"https://www.zbmath.org/authors/?q=ai:baskey.lipi"Rahaman, Farook"https://www.zbmath.org/authors/?q=ai:rahaman.farook"Aria, Anil K."https://www.zbmath.org/authors/?q=ai:aria.anil-kSummary: We present here a new class of singularity free interior solutions relevant for the description of realistic anisotropic compact stellar objects with spherically symmetric matter distribution. In this geometric approach, specific choices of one of the metric functions and a selective anisotropic profile allow us to develop a stellar model by solving Einstein Field equations. The interior solutions thus obtained are matched with the Schwarzschild exterior metric over the bounding surface of a compact star. These matching conditions together with the condition that the radial pressure vanishes at the boundary are used to fix the model parameters. The different physical features for the developed model explicitly studied from the aspect of the pulsar 4U \(1820-30\) with its current estimated data (mass \(=1.46\pm 0.21~M\odot\) and radius \(=11.1\pm 1.8\) km [\textit{F. Özel} et al., ``The dense matter equation of state from neutron star radius and mass measurements'', Astrophys. J. 820, No. 1, Paper No. 28, 25 p. (2016)]. Analysis has shown that all the physical aspects are acceptable demanded for a physically admissible star and satisfy all the required physical conditions. The stability of the model is also explored in the context of causality conditions, adiabatic index, generalized Tolman-Oppenheimer-Volkov (TOV) equation, Buchdahl Condition and Herrera Cracking Method. To show that the developed model is compatible with a wide range of recently observed pulsars, various relevant physical variables are also highlighted in tabular form. The data studied here are in agreement with the observation of gravitational waves from the first binary merger event. Assuming a particular surface density \((7.5\times 10^{14}\text{ gm cm}^{-3})\), the mass-radius \((M-b)\) relationship and the radius-central density relationship \((b-\rho(0))\) of the compact stellar object are analyzed for this model. Additionally, comparing the results with a slow rotating configuration, we have also discussed moment of inertia and the time period using Bejger-Haensel idea.Particle motion in a space-time of a 3D Einstein gravity with torsionhttps://www.zbmath.org/1483.830052022-05-16T20:40:13.078697Z"Kaya, R."https://www.zbmath.org/authors/?q=ai:kaya.rustem"Özçelik, H. T."https://www.zbmath.org/authors/?q=ai:ozcelik.hasan-tuncaySummary: We analyze the motion of both massive and massless particles in a model with space-time of 3D Einstein gravity with torsion. We consider the spinor field and the massless scalar field as the source of torsion respectively. Following the Hamilton-Jacobi formalism, we investigate the effective potential of radial motion for test particles in a homogeneous and isotropic space-time with torsion. We show that there are no stable circular orbits for massive and massless particles in the Einstein gravity with torsion induced by the spinor field, in a space-time with two spatial and one time dimensions. In the case of massive particles, we show that stable orbits exist in 3D Einstein gravity with torsion induced by the scalar field.Possible existence of a third fundamental long-range forcehttps://www.zbmath.org/1483.830072022-05-16T20:40:13.078697Z"Nakanishi, Noboru"https://www.zbmath.org/authors/?q=ai:nakanishi.noboru"Yoshida, Ritsu"https://www.zbmath.org/authors/?q=ai:yoshida.ritsuSummary: It is inferred that, in addition to the Coulomb and Newtonian forces, there should exist a third fundamental long-range force, which acts between intrinsic angular momenta. This inference is based on the quantum Einstein gravity, that is, the manifestly-covariant, BRS-invariant, canonically quantized theory of general relativity. The form of the potential of the third fundamental long-range force is determined by calculating the non-relativistic limit of the Bethe-Salpeter kernel in the lowest-order perturbation theory. The observability of this force is also discussed.Quasinormal resonances of rapidly-spinning Kerr black holes and the universal relaxation boundhttps://www.zbmath.org/1483.830102022-05-16T20:40:13.078697Z"Hod, Shahar"https://www.zbmath.org/authors/?q=ai:hod.shaharSummary: The universal relaxation bound suggests that the relaxation times of perturbed thermodynamical systems is bounded from below by the simple time-times-temperature (TTT) quantum relation \(\tau \times T \geq \frac{\hbar}{\pi}\). It is known that some perturbation modes of near-extremal Kerr black holes in the regime \(M T_{\mathrm{BH}}/\hbar \ll m^{-2}\) are characterized by normalized relaxation times \(\pi \tau \times T_{\mathrm{BH}}/\hbar\) which, in the approach to the limit \(M T_{\mathrm{BH}}/\hbar\to 0\), make infinitely many oscillations with a tiny constant amplitude around 1 and therefore cannot be used directly to verify the validity of the TTT bound in the entire parameter space of the black-hole spacetime (Here \(\{T_{\mathrm{BH}}, M\}\) are respectively the Bekenstein-Hawking temperature and the mass of the black hole, and \(m\) is the azimuthal harmonic index of the linearized perturbation mode). In the present compact paper we explicitly prove that all rapidly-spinning Kerr black holes respect the TTT relaxation bound. In particular, using analytical techniques, it is proved that all black-hole perturbation modes in the complementary regime \(m^{-1} \ll M T_{\mathrm{BH}}/\hbar\ll 1\) are characterized by relaxation times with the simple dimensionless property \(\pi \tau \times T_{\mathrm{BH}}/\hbar\geq 1\).Modifications to the signal from a gravitational wave event due to a surrounding shell of matterhttps://www.zbmath.org/1483.830162022-05-16T20:40:13.078697Z"Naidoo, Monos"https://www.zbmath.org/authors/?q=ai:naidoo.monos"Bishop, Nigel T."https://www.zbmath.org/authors/?q=ai:bishop.nigel-t"van der Walt, Petrus J."https://www.zbmath.org/authors/?q=ai:van-der-walt.petrus-jSummary: In previous work, we established theoretical results concerning the effect of matter shells surrounding a gravitational wave (GW) source, and we now apply these results to astrophysical scenarios. Firstly, it is shown that GW echoes that are claimed to be present in LIGO data of certain events, could not have been caused by a matter shell. However, it is also shown that there are scenarios in which matter shells could make modifications of order a few percent to a GW signal; these scenarios include binary black hole mergers, binary neutron star mergers, and core collapse supernovae.Loop quantum gravity and cosmological constanthttps://www.zbmath.org/1483.830252022-05-16T20:40:13.078697Z"Zhang, Xiangdong"https://www.zbmath.org/authors/?q=ai:zhang.xiangdong"Long, Gaoping"https://www.zbmath.org/authors/?q=ai:long.gaoping"Ma, Yongge"https://www.zbmath.org/authors/?q=ai:ma.yonggeSummary: A one-parameter regularization freedom of the Hamiltonian constraint for loop quantum gravity is analyzed. The corresponding spatially flat, homogenous and isotropic model includes the two well-known models of loop quantum cosmology as special cases. The quantum bounce nature is tenable in the generalized cases. For positive value of the regularization parameter, the effective Hamiltonian leads to an asymptotic de-Sitter branch of the Universe connecting to the standard Friedmann branch by the quantum bounce. Remarkably, by suitably choosing the value of the regularization parameter, the observational cosmological constant can emerge at large volume limit from the effect of quantum gravity, and the effective Newtonian constant satisfies the experimental restrictions in the meantime.5D \(\mathcal{N} = 1\) super QFT: symplectic quivershttps://www.zbmath.org/1483.830262022-05-16T20:40:13.078697Z"Saidi, E. H."https://www.zbmath.org/authors/?q=ai:saidi.el-hassan"Drissi, L. B."https://www.zbmath.org/authors/?q=ai:drissi.lalla-btissamSummary: We develop a method to build new 5D \(\mathcal{N} = 1\) gauge models based on Sasaki-Einstein manifolds \(Y^{p, q}\). These models extend the standard 5D ones having a unitary \(\mathrm{SU}(p)_q\) gauge symmetry based on \(Y^{p, q} \). Particular focus is put on the building of a gauge family with symplectic \(\mathrm{SP}(2r, \mathbb{R})\) symmetry. These super QFTs are embedded in M-theory compactified on folded toric Calabi-Yau threefolds \(\hat{X}(Y^{2r, 0})\) constructed from conical \(Y^{2r, 0}\). By using outer-automorphism symmetries of 5D \(\mathcal{N} = 1\) BPS quivers with unitary \(\mathrm{SU}(2r)\) gauge invariance, we also construct BPS quivers with symplectic \(\mathrm{SP}(2r, \mathbb{R})\) gauge symmetry. Other related aspects are discussed.QNMs of branes, BHs and fuzzballs from quantum SW geometrieshttps://www.zbmath.org/1483.830352022-05-16T20:40:13.078697Z"Bianchi, Massimo"https://www.zbmath.org/authors/?q=ai:bianchi.massimo"Consoli, Dario"https://www.zbmath.org/authors/?q=ai:consoli.dario"Grillo, Alfredo"https://www.zbmath.org/authors/?q=ai:grillo.alfredo"Morales, Francisco"https://www.zbmath.org/authors/?q=ai:morales.franciscoSummary: QNMs govern the linear response to perturbations of BHs, D-branes and fuzzballs and the gravitational wave signals in the ring-down phase of binary mergers. A remarkable connection between QNMs of neutral BHs in 4d and quantum SW geometries describing the dynamics of \(\mathcal{N} = 2\) SYM theories has been recently put forward. We extend the gauge/gravity dictionary to a large class of gravity backgrounds including charged and rotating BHs of Einstein-Maxwell theory in \(d = 4\), 5 dimensions, D3-branes, D1D5 `circular' fuzzballs and smooth horizonless geometries; all related to \(\mathcal{N} = 2\) SYM with a single \(SU(2)\) gauge group and fundamental matter. We find that photon-spheres, a common feature of all examples, are associated to degenerations of the classical elliptic SW geometry whereby a cycle pinches to zero size. Quantum effects resolve the singular geometry and lead to a spectrum of quantized energies, labelled by the overtone number \(n\). We compute the spectrum of QNMs using exact WKB quantization, geodetic motion and numerical simulations and show excellent agreement between the three methods. We explicitly illustrate our findings for the case D3-brane QNMs.Entropy of Reissner-Nordström-like black holeshttps://www.zbmath.org/1483.830362022-05-16T20:40:13.078697Z"Blagojević, M."https://www.zbmath.org/authors/?q=ai:blagojevic.milutin"Cvetković, B."https://www.zbmath.org/authors/?q=ai:cvetkovic.branislavSummary: In Poincaré gauge theory, black hole entropy is defined canonically by the variation of a boundary term \(\Gamma_H\), located at horizon. For a class of static and spherically symmetric black holes in vacuum, the explicit formula reads \(\delta \Gamma_H = T \delta S\), where \(T\) is black hole temperature and \(S\) entropy. Here, we analyze a new member of the same class, the Reissner-Nordström-like black hole with torsion [\textit{ J. A.R. Cembranos} and [\textit{J. G. Valcarcel}, ``New torsion black hole solutions in Poincaré gauge theory,'' J. Cosmol. Astropart. Phys., 01, Article 014 (2017; \url{doi:10.1088/1475-7516/2017/01/014})], where the electric charge of matter is replaced by a gravitational parameter, induced by the existence of torsion. This parameter affects \(\delta \Gamma_H\) in a way that ensures the validity of the first law.Black hole in Nielsen-Olesen vortexhttps://www.zbmath.org/1483.830432022-05-16T20:40:13.078697Z"Ghosh, Kumar J. B."https://www.zbmath.org/authors/?q=ai:ghosh.kumar-jang-bahadurSummary: In this article, we calculate the classical vortex solution of a spontaneously broken gauge theory interacting with gravity in (2+1)-dimension. We also calculate the conditions for the formation of a (2+1)-dimensional black hole due to magnetic vortex (a Nielsen-Olesen vortex). The semiclassical Hawking temperature for this black hole is calculated, where we see that the temperature of a BTZ black hole increases or decreases without changing the size of the horizon if we insert the magnetic vortex fields in the black hole. Finally, the first law of black hole thermodynamics is described for this particular solution, which shows that the additional work terms from the scalar and gauge fields compensate the change in the temperature relative to its usual value for the BTZ solution.Stability analysis of geodesics and quasinormal modes of a dual stringy black hole via Lyapunov exponentshttps://www.zbmath.org/1483.830452022-05-16T20:40:13.078697Z"Giri, Shobhit"https://www.zbmath.org/authors/?q=ai:giri.shobhit"Nandan, Hemwati"https://www.zbmath.org/authors/?q=ai:nandan.hemwatiSummary: We investigate the stability of both timelike as well as null circular geodesics in the vicinity of a dual (3+1) dimensional stringy black hole (BH) spacetime by using an excellent tool so-called Lyapunov exponent. The proper time \((\tau)\) Lyapunov exponent \((\lambda_p)\) and coordinate time \((t)\) Lyapunov exponent \((\lambda_c)\) are explicitly derived to analyze the stability of equatorial circular geodesics for the stringy BH spacetime with \textit{electric charge} parameter \((\alpha )\) and \textit{magnetic charge} parameter \((Q)\). By computing
these exponents for both the cases of BH spacetime, it is observed that the coordinate time Lyapunov exponent of magnetically charged stringy BH for both timelike and null geodesics are independent of magnetic charge parameter \((Q)\). The variation of the ratio of Lyapunov exponents with radius of timelike circular orbits \((r_0/M)\) for both the cases of stringy BH are presented. The behavior of instability exponent for null circular geodesics with respect to charge parameters \((\alpha\) and \(Q)\) are also observed for both the cases of BH. Further, by establishing a relation between quasinormal modes (QNMs) and parameters related to null circular geodesics (like angular frequency and Lyapunov exponent), we deduced the QNMs (or QNM frequencies) for a massless scalar field perturbation around \textit{both} the cases of stringy BH spacetime in the eikonal limit. The variation of scalar field potential with charge parameters and angular momentum of perturbation \((l)\) are visually presented and discussed accordingly.An alternative to the Teukolsky equationhttps://www.zbmath.org/1483.830472022-05-16T20:40:13.078697Z"Hatsuda, Yasuyuki"https://www.zbmath.org/authors/?q=ai:hatsuda.yasuyukiSummary: We conjecture a new ordinary differential equation exactly isospectral to the radial component of the homogeneous Teukolsky equation. We find this novel relation by a hidden symmetry implied from a four-dimensional \(\mathcal{N}=2\) supersymmetric quantum chromodynamics. Our proposal is powerful both in analytical and in numerical studies. As an application, we derive high-order perturbative series of quasinormal mode frequencies in the slowly rotating limit. We also test our result numerically by comparing it with a known technique.Correspondence between quasinormal modes and the shadow radius in a wormhole spacetimehttps://www.zbmath.org/1483.830502022-05-16T20:40:13.078697Z"Jusufi, Kimet"https://www.zbmath.org/authors/?q=ai:jusufi.kimetSummary: In this paper we study the correspondence between the real part of quasinormal modes and the shadow radius in a wormhole spacetime. Firstly we consider the above correspondence in a static and spherically symmetric wormhole spacetime and then explore this correspondence numerically by considering different wormhole models having specific redshift functions. To this end, we generalize this correspondence to the rotation wormhole spacetime and calculate the typical shadow radius of the rotating wormhole when viewed from the equatorial plane. We argue that due to the rotation and depending on the specific model, the typical shadow radius can increase or decrease and a reflecting point exists. Finally, we discuss whether a wormhole can mimic the black hole due to it's shadow. In the light of the EHT data, we find the upper and lower limits of the wormhole throat radius in the galactic center M87.Superradiance and stability of Kerr black hole enclosed by anisotropic fluid matterhttps://www.zbmath.org/1483.830512022-05-16T20:40:13.078697Z"Khodadi, Mohsen"https://www.zbmath.org/authors/?q=ai:khodadi.mohsen"Pourkhodabakhshi, Reza"https://www.zbmath.org/authors/?q=ai:pourkhodabakhshi.rezaSummary: Focusing on the rotating black hole (BH) surrounded by the anisotropic fluid matters; radiation, dust, and dark matter, we study the massive scalar superradiant scattering and the stability in the Kiselev spacetime. Superradiance behavior is dependent on the intensity parameter of the anisotropic matter \(K\) in the Kiselev spacetime. By adopting the manifest of low-frequency and low-mass for the scalar perturbation, we find \(K < 0\) enhances the superradiance scattering within the broader frequency range, compared to \(K = 0\) while \(K > 0\) suppresses within the narrower frequency range. As a result, the radiation and dark matter around the rotating BH act as amplifier and attenuator for the massive scalar superradiance, respectively. This is while the dust has a twofold role because of admitting both signs of \(K\). Through stability analysis in the light of the BH bomb mechanism, we show in the presence of dark matter, the instability regime of standard Kerr BH (\(K = 0\)) gets improved in favor of stabilization while the radiation and dust do not affect it. In other words, by taking the dark matter fluid around BH into account, we obtain a broader regime that allows the massive scalar field dynamic to enjoy superradiant stability.Corrections to Hawking radiation and Bekenstein-Hawking entropy of novel four-dimensional black holes in Gauss-Bonnet gravityhttps://www.zbmath.org/1483.830532022-05-16T20:40:13.078697Z"Li, Gu-Qiang"https://www.zbmath.org/authors/?q=ai:li.guqiang"Mo, Jie-Xiong"https://www.zbmath.org/authors/?q=ai:mo.jie-xiong"Zhuang, Yi-Wen"https://www.zbmath.org/authors/?q=ai:zhuang.yi-wenSummary: We make use of the Hamilton-Jacobi and Parikh-Wilczek methods to investigate the Hawking radiation from the event horizon of a new charged anti-de Sitter black hole in four-dimensional Gauss-Bonnet gravity space-time. Both the tunneling rate of charged particles and the Bekenstein-Hawking entropy are evaluated. The emission spectrum is an impure thermal one and consistent with an underlying unitary theory. There is no difference between the emission rate of massive particle and that of massless one. The entropy is modified by a logarithmic term so that the area law of the black hole entropy is violated. It satisfies the first law of black hole thermodynamics and has the same expression as that calculated by Loop Quantum Gravity and String Theory. When the Gauss-Bonnet coupling coefficient is equal to zero, the logarithmic correction vanishes and the Bekenstein-Hawking relation in general relativity is recovered. So our results show the effects of the Gauss-Bonnet modified gravity on the Bekenstein-Hawking entropy and Hawking radiation.Aliasing instabilities in the numerical evolution of the Einstein field equationshttps://www.zbmath.org/1483.830572022-05-16T20:40:13.078697Z"Meringolo, C."https://www.zbmath.org/authors/?q=ai:meringolo.c"Servidio, S."https://www.zbmath.org/authors/?q=ai:servidio.sergioSummary: The Einstein field equations of gravitation are characterized by cross-scale, high-order nonlinear terms, representing a challenge for numerical modeling. In an exact spectral decomposition, high-order nonlinearities correspond to a convolution that numerically might lead to aliasing instabilities. We present a study of this problem, in vacuum conditions, based on the \(3+1\) Baumgarte-Shibata-Shapiro-Nakamura (BSSN) formalism. We inspect the emergence of numerical artifacts, in a variety of conditions, by using the Spectral-FIltered Numerical Gravity codE (\texttt{SFINGE}) -- a pseudo-spectral algorithm, based on a classical (Cartesian) Fourier decomposition. By monitoring the highest \(k\)-modes of the dynamical
fields, we identify the culprits of the aliasing and propose procedures that cure such instabilities, based on the suppression of the aliased wavelengths. This simple algorithm, together with appropriate treatment of the boundary conditions, can be applied to a variety of gravitational problems, including those related to massive objects dynamics.Shadow and weak deflection angle of extended uncertainty principle black hole surrounded with dark matterhttps://www.zbmath.org/1483.830592022-05-16T20:40:13.078697Z"Pantig, Reggie C."https://www.zbmath.org/authors/?q=ai:pantig.reggie-c"Yu, Paul K."https://www.zbmath.org/authors/?q=ai:yu.paul-k-l"Rodulfo, Emmanuel T."https://www.zbmath.org/authors/?q=ai:rodulfo.emmanuel-t"Övgün, Ali"https://www.zbmath.org/authors/?q=ai:ovgun.aliSummary: In this paper, we discuss the possible effects of dark matter on a Schwarzschild black hole with the correction of extended uncertainty principle (EUP), such as the parameter \(\alpha\) and the large fundamental length scale \(L_\ast\). In particular, we surround the EUP black hole of mass \(m\) with a static spherical shell of dark matter described by the parameters mass \(M\), inner radius \(r_s\), and thickness \(\Delta r_s\). In this study, we find that there is no deviation in the event horizon, which readily implies that the black hole temperature due to the Hawking radiation is independent of any dark matter concentration. In addition, we show some effects of the EUP parameter on the innermost stable circular orbit (ISCO) radius of time-like particles, photon sphere, shadow radius, and weak deflection angle. It is found that time-like orbits are affected by deviation of low values of mass \(M\). A greater dark matter density is needed to have remarkable effects on the null orbits. Using the analytic expression for the shadow radius and the approximation \(\Delta r_s\gg r_s\), it is revealed that \(L_\ast\) should not be lower than \(2m\). To broaden the scope of this study, we also calculate the analytic expression for the weak deflection angle using the Ishihara et al. method [\textit{A. Ishihara} et al., ``Gravitational bending angle of light for finite distance and the Gauss-Bonnet theorem'', Phys. Rev. D 94, No. 8, Article ID 084015, 9 p. (2016; \url{doi:10.1103/PhysRevD.94.084015})]. As a result, we show that \(\Delta r_s\) is improved by a factor of \((1+4\alpha m^2/L_\ast^2)\) due to the EUP correction parameters. The calculated shadow radius and weak deflection angle are then compared using the estimated values of the galactic mass from Sgr A*, M87, and UGC 7232, as well as the mass of the supermassive black hole at their center.Energy formula for Newman-unti-tamburino class of black holeshttps://www.zbmath.org/1483.830602022-05-16T20:40:13.078697Z"Pradhan, Parthapratim"https://www.zbmath.org/authors/?q=ai:pradhan.parthapratimSummary: We compute the \textit{surface energy} \((\mathcal{E}_s^{\pm})\), \textit{the rotational energy} \((\mathcal{E}_r^\pm)\) \textit{and the electromagnetic energy} \((\mathcal{E}_{em}^\pm)\) for Newman-Unti-Tamburino (NUT) class of black hole having the event horizon \((\mathcal{H}^+)\) and the Cauchy horizon \((\mathcal{H}^-)\). Remarkably, we find that the \textit{mass parameter can be expressed as sum of three energies, i.e.,} \(M=\mathcal{E}_s^{\pm}+\mathcal{E}_r^{\pm}+\mathcal{E}_{em}^{\pm}\). It has been \textit{tested} for Taub-NUT black hole, Reissner-Nordström-Taub-NUT black hole, Kerr-Taub-NUT black hole and Kerr-Newman-Taub-NUT black hole. In each case of black hole, we find that \textit{the sum of these energies is equal to the Komar mass}. It is plausible only due to the introduction of new conserved charges i. e. \(J_N=M\,N\) (where \(M=m\) is the Komar mass and \(N=n\) is the gravitomagnetic charge), which is closely analogue to the Kerr-like angular momentum parameter \(J=a\,M\).Greybody factor for a rotating Bardeen black hole by perfect fluid dark matterhttps://www.zbmath.org/1483.830642022-05-16T20:40:13.078697Z"Sharif, M."https://www.zbmath.org/authors/?q=ai:sharif.muhammad-a-r|sharif.mhd-saeed|sharif.masoud"Shaukat, Sulaman"https://www.zbmath.org/authors/?q=ai:shaukat.sulamanSummary: In this paper, the greybody factor is studied analytically for a rotating regular Bardeen black hole surrounded by perfect fluid dark matter. Firstly, we examine the behavior of effective potential by using the radial equation of motion developed from the Klein-Gordon equation. We then consider tortoise coordinate to convert the radial equation into Schrödinger form equation. We solve the radial equation of motion and obtain two different asymptotic solutions in terms of hypergeometric function measured at distinct regimes so called near and far-field horizons. These solutions are smoothly matched over the whole radial coordinate in an intermediate regime to check their viability. Finally, we measure the absorption probability for massless scalar field and examine the effect of perfect fluid dark matter. It is concluded that both the effective potential and greybody factor increase with perfect fluid dark matter.Covariant Hamiltonian formalism for \(F(R)\)-gravityhttps://www.zbmath.org/1483.830702022-05-16T20:40:13.078697Z"Klusoň, J."https://www.zbmath.org/authors/?q=ai:kluson.josef"Matouš, B."https://www.zbmath.org/authors/?q=ai:matous.bSummary: In this short note we apply Weyl-De Donder formalism, also known as covariant Hamiltonian formalism, for \(F(R)\)-gravity. We derive covariant Hamiltonian and derive corresponding equations of motion.Gauge field theory vacuum and cosmological inflation without scalar fieldhttps://www.zbmath.org/1483.830752022-05-16T20:40:13.078697Z"Savvidy, George"https://www.zbmath.org/authors/?q=ai:savvidy.george-kSummary: We derive the quantum energy-momentum tensor and the corresponding quantum equation of state for gauge field theory using the effective Lagrangian approach. The energy-momentum tensor has a term proportional to the space-time metric and provides a finite non-diverging contribution to the effective cosmological term. This allows to investigate the influence of the gauge field theory vacuum polarisation on the evolution of Friedmann cosmology, inflation and primordial gravitational waves. The Type I-IV solutions of the Friedmann equations induced by the gauge field theory vacuum polarisation provide an alternative inflationary mechanism and a possibility for late-time acceleration. The Type II solution of the Friedmann equations generates the initial exponential expansion of the universe of finite duration and the Type IV solution demonstrates late-time acceleration. The solutions fulfil the necessary conditions for the amplification of primordial gravitational waves.Straightforward Hamiltonian analysis of \textit{BF} gravity in \(n\) dimensionshttps://www.zbmath.org/1483.830772022-05-16T20:40:13.078697Z"Montesinos, Merced"https://www.zbmath.org/authors/?q=ai:montesinos.merced"Escobedo, Ricardo"https://www.zbmath.org/authors/?q=ai:escobedo.ricardo"Celada, Mariano"https://www.zbmath.org/authors/?q=ai:celada.marianoSummary: We perform, in a manifestly \(\mathrm{SO}(n-1,1) [\mathrm{SO}(n)]\) covariant fashion, the Hamiltonian analysis of general relativity in \(n\) dimensions written as a constrained \textit{BF} theory. We solve the constraint on the \(B\) field in a way naturally adapted to the foliation of the spacetime that avoids explicitly the introduction of the vielbein. This leads to a form of the action involving a presymplectic structure, which is reduced by doing a suitable parametrization of the connection and then, after integrating out some auxiliary fields, the Hamiltonian form involving only first-class constraints is obtained.Noether symmetry in Newtonian dynamics and cosmologyhttps://www.zbmath.org/1483.830852022-05-16T20:40:13.078697Z"Guendelman, E. I."https://www.zbmath.org/authors/?q=ai:guendelman.eduardo-i"Zamlung, E."https://www.zbmath.org/authors/?q=ai:zamlung.e"Benisty, D."https://www.zbmath.org/authors/?q=ai:benisty.davidSummary: A new symmetry for Newtonian Dynamics is analyzed, this corresponds to going to an accelerated frame, which introduces a constant gravitational field into the system and subsequently. We consider the addition of a linear contribution to the gravitational potential \(\phi\) which can be used to cancel the gravitational field induced by going to the accelerated from, the combination of these two operations produces then a symmetry. This symmetry leads then to a Noether current which is conserved. The conserved charges are analyzed in special cases. The charges may not be conserved if the Noether current produces flux at infinity, but such flux can be eliminated by going to the CM (center of mass) system in the case of an isolated system. In the CM frame the Noether charge vanishes, Then we study connection between the Cosmological Principle and the Newtonian Dynamics which was formulated via a symmetry \textit{D. Benisty} and \textit{E. I. Guendelman} [Mod. Phys. Lett. A 35, No. 16, Article ID 2050131, 7 p. (2020; Zbl 1435.85006)] of this type, but without an action formulation. Homogeneous behavior for the coordinate system relevant to cosmology leads to a zero Noether current and the requirement of the Newtonian potential to be invariant under the symmetry in this case yields the Friedmann equations, which appear as a consistency condition for the symmetry.Nonstaticity with type II, III, or IV matter field in \(f(R_{\mu\nu\rho\sigma},g^{\mu\nu})\) gravityhttps://www.zbmath.org/1483.830882022-05-16T20:40:13.078697Z"Maeda, Hideki"https://www.zbmath.org/authors/?q=ai:maeda.hidekiSummary: In all \(n(\ge 3)\)-dimensional gravitation theories whose Lagrangians are functions of the Riemann tensor and metric, we show that static solutions are absent unless the total energy-momentum tensor for matter fields is of type I in the Hawking-Ellis classification. In other words, there is no hypersurface-orthogonal timelike Killing vector in a spacetime region with an energy-momentum tensor of type II, III, or IV. This asserts that, if back-reaction is taken into account to give a self-consistent solution, ultra-dense regions with a semiclassical type-IV matter field cannot be static even with higher-curvature correction terms. As a consequence, a static Planck-mass relic is possible as a final state of an evaporating black hole only if the semiclassical total energy-momentum tensor is of type I.The evolution of binary neutron star post-merger remnants: a reviewhttps://www.zbmath.org/1483.850012022-05-16T20:40:13.078697Z"Sarin, Nikhil"https://www.zbmath.org/authors/?q=ai:sarin.nikhil"Lasky, Paul D."https://www.zbmath.org/authors/?q=ai:lasky.paul-dSummary: Two neutron stars merge somewhere in the Universe approximately every 10 to 100 s, creating violent explosions potentially observable in gravitational waves and across the electromagnetic spectrum. The transformative coincident gravitational-wave and electromagnetic observations of the binary neutron star merger GW170817 gave invaluable insights into these cataclysmic collisions, probing bulk nuclear matter at supranuclear
densities, the jet structure of gamma-ray bursts, the speed of gravity, and the cosmological evolution of the local Universe, among other things. Despite the wealth of information, it is still unclear when the remnant of GW170817 collapsed to form a black hole. Evidence from other short gamma-ray bursts indicates a large fraction of mergers may form long-lived neutron stars. We review what is known observationally and theoretically about binary neutron star post-merger remnants. From a theoretical perspective, we review our understanding of the evolution of short- and long-lived merger remnants, including fluid, magnetic-field, and temperature evolution. These considerations impact prospects of detection of gravitational waves from either short- or long-lived neutron star remnants which potentially allows for new probes into the hot nuclear equation of state in conditions inaccessible in terrestrial experiments. We also review prospects for determining post-merger physics from current and future electromagnetic observations, including kilonovae and late-time X-ray and radio afterglow observations.Spinning gauged boson and Dirac stars: a comparative studyhttps://www.zbmath.org/1483.850032022-05-16T20:40:13.078697Z"Herdeiro, C."https://www.zbmath.org/authors/?q=ai:herdeiro.carlos-a-r"Perapechka, I."https://www.zbmath.org/authors/?q=ai:perapechka.ilya"Radu, E."https://www.zbmath.org/authors/?q=ai:radu.eugen"Shnir, Ya."https://www.zbmath.org/authors/?q=ai:shnir.yakov-m|shnir.yashaSummary: Scalar boson stars and Dirac stars are solitonic solutions of the Einstein-Klein-Gordon and Einstein-Dirac classical equations, respectively. Despite the different bosonic \textit{vs}. fermionic nature of the matter field, these solutions to the classical field equations have been shown to have qualitatively similar features [1]. In particular, for spinning stars the most fundamental configurations can be in both cases toroidal, unlike spinning Proca stars that are spheroidal[\textit{C. Herdeiro} et al., ibid. 797, Article ID 134845, 8 p. (2019; Zbl 1427.83010)]. In this paper we gauge the scalar and Dirac fields, by minimally coupling them to standard electromagnetism. We explore the impact of the gauge coupling on the resulting solutions. One of the most relevant difference concerns the gyromagnetic ratio, which for the scalar stars takes values around 1, whereas for Dirac stars takes values around 2.Galactic clustering under power-law modified Newtonian potentialhttps://www.zbmath.org/1483.850062022-05-16T20:40:13.078697Z"Khanday, Abdul W."https://www.zbmath.org/authors/?q=ai:khanday.abdul-w"Upadhyay, Sudhaker"https://www.zbmath.org/authors/?q=ai:upadhyay.sudhaker"Ganai, Prince A."https://www.zbmath.org/authors/?q=ai:ganai.prince-ahmadSummary: We estimate galaxy clustering under a modified gravitational potential. In particular, the modifications in gravitational potential energy occur due to a power-law and cosmological constant terms. We derive a canonical partition function for the system of galaxies interacting under such a modified gravitational potential. Moreover, we compute various thermodynamical equation of states for the system. We do comparative analysis in order to emphasize the effect of corrections on thermodynamics of the system. Interestingly, the modifications in thermodynamical quantities are embedded in clustering parameter only.Hawking-like radiation of charged particles via tunneling across the lightcylinder of a rotating magnetospherehttps://www.zbmath.org/1483.850072022-05-16T20:40:13.078697Z"Li, Huiquan"https://www.zbmath.org/authors/?q=ai:li.huiquanSummary: In rotating magnetospheres planted on compact objects, there usually exist lightcylinders (LC), beyond which the rotation speed of the magnetic field lines exceeds the speed of light. The LC is a close analog to the horizon in gravity, and is a casual boundary for charged particles that are restricted to move along the magnetic field lines. In this work, it is proposed that there should be Hawking-like radiation of charged particles from the LC of a rotating magnetosphere from the point of view of tunneling by using the field sheet metric.Aspects of GRMHD in high-energy astrophysics: geometrically thick disks and tori agglomerates around spinning black holeshttps://www.zbmath.org/1483.850102022-05-16T20:40:13.078697Z"Pugliese, D."https://www.zbmath.org/authors/?q=ai:pugliese.daniela"Montani, G."https://www.zbmath.org/authors/?q=ai:montani.giovanniSummary: This work focuses on some key aspects of the general relativistic (GR) -- magneto-hydrodynamic (MHD) applications in high-energy astrophysics. We discuss the relevance of the GRHD counterparts formulation exploring the geometrically thick disk models and constraints of the GRMHD shaping the physics of accreting configurations. Models of clusters of tori orbiting a central super-massive black hole (\textbf{SMBH}) are described. These orbiting tori aggregates form sets of geometrically thick, pressure supported, perfect fluid tori, associated to complex instability processes including tori collision emergence and
empowering a wide range of activities related expectantly to the embedding matter environment of Active Galaxy Nuclei. Some notes are included on aggregates combined with proto-jets, represented by open cusped solutions associated to the geometrically thick tori.
This exploration of some key concepts of the GRMHD formulation in its applications to High-Energy Astrophysics starts with the discussion of the initial data problem for a most general Einstein-Euler-Maxwell system addressing the problem with a relativistic geometric background. The system is then set in quasi linear hyperbolic form, and the reduction procedure is argumented. Then, considerations follow on the analysis of the stability problem
for self-gravitating systems with determined symmetries considering the perturbations also of the geometry part on the quasi linear hyperbolic onset. Thus we focus on the ideal GRMHD and self-gravitating plasma ball. We conclude with the models of geometrically thick GRHD disks gravitating around a Kerr \textbf{SMBH} in their GRHD formulation and including in the force balance equation of the disks the influence of a toroidal magnetic field, determining its impact in tori topology and stability.Copositivity for 3rd-order symmetric tensors and applicationshttps://www.zbmath.org/1483.901072022-05-16T20:40:13.078697Z"Liu, Jiarui"https://www.zbmath.org/authors/?q=ai:liu.jiarui"Song, Yisheng"https://www.zbmath.org/authors/?q=ai:song.yisheng|song.yisheng.1Summary: The strict copositivity of 4th-order symmetric tensor may apply to detect vacuum stability of general scalar potential. For finding analytical expressions of (strict) copositivity of 4th-order symmetric tensor, we may reduce its order to 3rd order to better deal with it. So, it is provided several analytically sufficient conditions for the copositivity of 3rd-order 2-dimensional (3-dimensional) symmetric tensors. Subsequently, applying these conclusions to 4th-order tensors, the analytically sufficient conditions of copositivity are proved for 4th-order 2-dimensional and 3-dimensional symmetric tensors. Finally, we apply these results to present analytical vacuum stability conditions for vacuum stability for \(\mathbb{Z}_3\) scalar dark matter.Research on early warning algorithm for economic management based on Lagrangian fractional calculushttps://www.zbmath.org/1483.910602022-05-16T20:40:13.078697Z"Su, Xin"https://www.zbmath.org/authors/?q=ai:su.xin"Yu, Keshu"https://www.zbmath.org/authors/?q=ai:yu.keshu"Yu, Miao"https://www.zbmath.org/authors/?q=ai:yu.miaoSummary: The occurrence of economic management crisis has seriously affected the production and operation of enterprises, the stability of capital markets and even the economic security of the entire country and the world. The use of higher mathematics in economic management is very beneficial to the economic restructuring. For example, in the Lagrangian method for solving the constraint optimization problem, the correlation function can be listed in the Lagrangian fractional calculus equation for the economic management early warning problem with many independent variables. Then take one of the factors as the dependent variable and other factors as fixed constants, and bring them into the Lagrangian fractional calculus equation, you can find the variable solution and get the extreme value of the economic management early warning algorithm. Therefore, this paper combines normative research and empirical research to study the algorithm design, theoretical analysis and numerical experiments of Lagrangian-based methods for solving constrained optimization problems. The Lagrangian fractional calculus method is used to evaluate the early warning algorithm of economic management, improve the prediction accuracy and practicability of the model, and conduct empirical research. It is expected to find a way to effectively determine whether a listed company is caught in an economic management crisis and provide early warning for the listed company's own management.Vibrational mono-/bi-resonance and wave propagation in FitzHhugh-Nagumo neural systems under electromagnetic inductionhttps://www.zbmath.org/1483.920372022-05-16T20:40:13.078697Z"Ge, Mengyan"https://www.zbmath.org/authors/?q=ai:ge.mengyan"Lu, Lulu"https://www.zbmath.org/authors/?q=ai:lu.lulu"Xu, Ying"https://www.zbmath.org/authors/?q=ai:xu.ying"Mamatimin, Rozihajim"https://www.zbmath.org/authors/?q=ai:mamatimin.rozihajim"Pei, Qiming"https://www.zbmath.org/authors/?q=ai:pei.qiming"Jia, Ya"https://www.zbmath.org/authors/?q=ai:jia.yaSummary: In this paper, an modified FitzHugh-Nagumo (FHN) neural model was employed to investigate the vibrational resonance (VR) phenomenon, the collective behaviors, and the transmission of weak low-frequency (LF) signal driven by high-frequency (HF) stimulus under the action of different electromagnetic induction in single FHN neuron and feed-forward feedback network (FFN) system, respectively. For the single FHN system, by increasing the amplitude of HF stimulus, the phenomena of vibrational mono-/bi-resonance are observed, and the input weak signal and output of system are synchronized, and the information of the weak LF signal is amplified. For the FFN system, the phenomena of vibrational mono-/bi-resonances are also occurred, both frequency and amplitude of the HF stimulus play an important role in the vibrational bi-resonances and transmission of weak LF signal in the FHN neural FFN.Bearing-based formation manoeuvre control of nonholonomic multi-agent systemshttps://www.zbmath.org/1483.930222022-05-16T20:40:13.078697Z"Li, Xiaolei"https://www.zbmath.org/authors/?q=ai:li.xiaolei"Er, Meng Joo"https://www.zbmath.org/authors/?q=ai:er.mengjoo"Yang, Guanghong"https://www.zbmath.org/authors/?q=ai:yang.guang-hong"Wang, Ning"https://www.zbmath.org/authors/?q=ai:wang.ningSummary: This paper concerns on the bearing-based leader-follower formation manoeuvre control problem for two- (2D) and three-dimensional (3D) multi-agent systems with nonholonomic constraint. The target formation is defined by relative-bearing measurements, which, for example, can be obtained from onboard cameras. The contributions of this paper are twofold. Firstly, a distributed formation manoeuvre control law is proposed for 2D nonholonomic agents according to the inter-bearing measurement. The multi-agent systems can achieve the desired formation which is defined by the bearings information. The formation manoeuvre can be achieved by steering at least two leaders. Secondly, the control law is nontrivially extended to 3D nonholonomic multi-agents systems. The leader-follower formation tracking problem can also be solved by the proposed proportional-integral control scheme. Simulation results for 2D and 3D nonholonomic multi-agents systems are presented. Experiments that used ground mobile robots verify the effectiveness of the proposed control laws.Principles of lossless adjustable one-portshttps://www.zbmath.org/1483.930762022-05-16T20:40:13.078697Z"Georgiou, Tryphon T."https://www.zbmath.org/authors/?q=ai:georgiou.tryphon-t"Jabbari, Faryar"https://www.zbmath.org/authors/?q=ai:jabbari.faryar"Smith, Malcolm C."https://www.zbmath.org/authors/?q=ai:smith.malcolm-cEditorial remark: No review copy delivered.Robust nonlinear attitude tracking control of an underactuated spacecraft under saturation and time-varying uncertaintieshttps://www.zbmath.org/1483.931092022-05-16T20:40:13.078697Z"Nadafi, Reza"https://www.zbmath.org/authors/?q=ai:nadafi.reza"Kabganian, Mansour"https://www.zbmath.org/authors/?q=ai:kabganian.mansourSummary: The three-axis attitude tracking control of an underactuated spacecraft in the large-angle maneuver was investigated in this study. As a major contribution of this paper, a robust controller was developed to achieve the perfect attitude tracking of the underactuated spacecraft with consideration of saturation and uncertainties. Interestingly, due to non-singularity of this design, it could relax the burden of limiting the initial condition of the quaternions. The stability analysis of the developed controller could be guaranteed by Lyapunov method as shown here. Overall, the simulation results indicate that the proposed controller has robustness against saturation, external perturbations, inertia uncertainties, and internal disturbances of actuators. As result, the controller was asymptotically stable under the combination of the soft saturation and the perturbations so that attitude parameters converged to the desired path within the 230 s. In this case, the saturation level was consumed 0.08 N.m. Also, it was still asymptotic stable under the hard saturation whose level is equal to 0.01 Nm, 12.5\% of the soft saturation level.A speed regulator for a force-driven cart-pole systemhttps://www.zbmath.org/1483.932052022-05-16T20:40:13.078697Z"Sandoval, Jesús"https://www.zbmath.org/authors/?q=ai:sandoval.jesus"Kelly, Rafael"https://www.zbmath.org/authors/?q=ai:kelly.rafael"Santibáñez, Víctor"https://www.zbmath.org/authors/?q=ai:santibanez.victorSummary: In this paper, we present a speed regulator for a force-driven cart-pole system. The proposed controller allows bringing the pole towards its upright position, while the cart moves asymptotically at desired constant speed, recovering the position regulation when we assign a desired constant position of the cart. The main motivation for addressing speed regulation is to broaden the scope of control of underactuated mechanical systems, because so far, the control of this class of mechanical systems has been focused primarily on position regulation; and therefore, there is few information and results available on broader control objectives, such as speed regulation. In particular, we design a speed regulator for the cart-pole system, as this system is one of the more representative test benches of underactuated mechanical system found in many automatic control research laboratories. Another novelty is the introduction of an alternative energy shaping approach for the velocity control design of a class of underactuated mechanical systems. A complete asymptotic stability analysis based on the Lyapunov theory and the Barbashin-Krasovskii theorem is presented. Local asymptotic stability is concluded. Simulation results upon a force-driven cart-pole model illustrate the performance of the proposed controller.Output constraints vibration control for a flexible aircraft wing with prescribed performancehttps://www.zbmath.org/1483.932512022-05-16T20:40:13.078697Z"Gao, Shiqi"https://www.zbmath.org/authors/?q=ai:gao.shiqi"Zhang, Yuanyuan"https://www.zbmath.org/authors/?q=ai:zhang.yuanyuan"Liu, Jinkun"https://www.zbmath.org/authors/?q=ai:liu.jinkunSummary: This study focuses on the vibration control and boundary output constraint problems for a flexible wing system. The coupled twist-bending dynamic model of the flexible wing contains several partial differential equations (PDEs) and ordinary differential equations (ODEs). With the help of prescribed performance functions, an innovative boundary controller is designed to achieve the vibration suppression without the violation of prescribed performance. The proposed controller can make the boundary deformations converge to an arbitrarily small residual set. In addition, a disturbance observer is proposed to eliminate the adverse effect caused by unknown external disturbances. Then the asymptotic stability of the closed-loop system is justified by the Lyapunov's direct method. Finally, numerical simulations are carried out to demonstrate the effectiveness of the proposed control scheme.Adaptive practical fast finite-time consensus protocols for multiple uncertain nonlinear mechanical systemshttps://www.zbmath.org/1483.932662022-05-16T20:40:13.078697Z"Cai, Mingjie"https://www.zbmath.org/authors/?q=ai:cai.mingjie"Xiang, Zhengrong"https://www.zbmath.org/authors/?q=ai:xiang.zhengrongSummary: In this paper, we study the design of a fast finite-time consensus protocol for multiple nonlinear mechanical systems with uncertainties and disturbance. Combining the theories of finite-time control and algebraic graph, a distributed adaptive fast finite-time consensus protocol is proposed in a recursive design way. In the designed control scheme, the unknown nonlinear functions are modelled by neural networks. With the help of fast finite-time boundedness lemma, the practical finite-time consensus of the multiple mechanical systems is proved. In the end, the validity of the proposed protocol is confirmed by a numerical example of multiple manipulators.Neural adaptive integral sliding mode control for attitude tracking of flexible spacecraft with signal quantisation and actuator nonlinearityhttps://www.zbmath.org/1483.932922022-05-16T20:40:13.078697Z"Liu, Qiuhong"https://www.zbmath.org/authors/?q=ai:liu.qiuhong"Liu, Ming"https://www.zbmath.org/authors/?q=ai:liu.ming.3"Shi, Yan"https://www.zbmath.org/authors/?q=ai:shi.yanSummary: This study investigates the neural adaptive integral sliding mode control for attitude tracking of flexible spacecraft, where unknown actuator nonlinearity, input quantisation and external disturbances are considered simultaneously. In this design, the hysteresis encoder-decoder scheme is employed between the controller and actuator side for signal quantisation. A quantised adaptive integral sliding mode control strategy is developed, where the neural network scheme is applied to approximate the unmeasurable rigid-flexible coupled nonlinear dynamics. The proposed control strategy can compensate for quantisation error, actuator faults, actuator dead-zone as well as external disturbances effectively, and guarantee the trajectory of the attitude tracking error converge to the equilibrium point along the designed sliding surface. Finally, a simulation example is conducted to demonstrate the validness of the developed quantised control strategy for flexible spacecraft attitude tracking problem.Connectivity-preserving-based distributed adaptive asymptotically synchronised tracking of networked uncertain nonholonomic mobile robots with actuator failures and unknown control directionshttps://www.zbmath.org/1483.933222022-05-16T20:40:13.078697Z"Xu, Yujing"https://www.zbmath.org/authors/?q=ai:xu.yujing"Wang, Chaoli"https://www.zbmath.org/authors/?q=ai:wang.chaoli"Yan, Weigang"https://www.zbmath.org/authors/?q=ai:yan.weigang"Lin, Mingfeng"https://www.zbmath.org/authors/?q=ai:lin.mingfeng"Tao, Jianguo"https://www.zbmath.org/authors/?q=ai:tao.jianguoSummary: This brief addresses a distributed adaptive asymptotically synchronous tracking problem based on guaranteed connectivity for networked uncertain nonholonomic mobile robots (NMRs) with actuator failures and unknown control directions. First, a radial basis function (RBF) neural network is used to approximate the unknown nonlinear functions, and a distributed nonlinear error surface is introduced to achieve synchronous tracking between NMRs and maintain the initial connectivity patterns. Then, a conditional inequality that allows multiple piecewise Nussbaum functions to achieve robust control is proposed to solve the problem of unknown actuator failures and unknown control directions. Moreover, the proposed protocol ensures that all signals in the closed-loop system are globally bounded and the tracking errors converge asymptotically to zero. Finally, a simulation example verifies the effectiveness of the proposed adaptive laws.Orbital stability analysis for perturbed nonlinear systems and natural entrainment via adaptive Andronov-Hopf oscillatorhttps://www.zbmath.org/1483.933292022-05-16T20:40:13.078697Z"Zhao, Jinxin"https://www.zbmath.org/authors/?q=ai:zhao.jinxin"Iwasaki, Tetsuya"https://www.zbmath.org/authors/?q=ai:iwasaki.tetsuyaEditorial remark: No review copy delivered.Immersion and invariance disturbance observer-based nonlinear discrete-time control for fully actuated mechanical systemshttps://www.zbmath.org/1483.933582022-05-16T20:40:13.078697Z"Adıgüzel, Fatih"https://www.zbmath.org/authors/?q=ai:adiguzel.fatih"Yalçın, Yaprak"https://www.zbmath.org/authors/?q=ai:yalcin.yaprakSummary: This paper addresses the attenuation problem of input disturbances in the control of fully actuated mechanical systems in the discrete-time setting. Firstly, a discrete-time disturbance estimator design with immersion and invariance (I\&I) approach is presented for the n-degrees of freedom (DOF) fully actuated mechanical systems. Then, a discrete-time combined feedback linearising and backstepping control is established that this controller uses the estimated disturbance information. Global asymptotic stability of the estimator and local asymptotic stability of the entire closed-loop system in an arbitrarily large compact set are shown utilising the Lyapunov stability theory. In order to show the effectiveness of the proposed composite observer-based discrete-time control method, it is applied to the 3-DOF robotic manipulator. Performance of proposed direct discrete-time combined feedback linearising and backstepping controller with discrete-time I\&I observer is compared with a direct discrete-time conventional second-order sliding mode controller with another discrete-time nonlinear disturbance observer via simulations. The superior performance of the proposed method is demonstrated with simulation results.Event-triggered leader-following consensus of multiple mechanical systems with switched dynamicshttps://www.zbmath.org/1483.933982022-05-16T20:40:13.078697Z"Liu, Yujiao"https://www.zbmath.org/authors/?q=ai:liu.yujiao"Tang, Rongqiang"https://www.zbmath.org/authors/?q=ai:tang.rongqiang"Zhou, Chao"https://www.zbmath.org/authors/?q=ai:zhou.chao"Xiang, Zhengrong"https://www.zbmath.org/authors/?q=ai:xiang.zhengrong"Yang, Xinsong"https://www.zbmath.org/authors/?q=ai:yang.xinsongSummary: This paper investigates the event-triggered leader-following consensus problem for a class of multiple mechanical systems with switched dynamics. Based on the graph theory, Lyapunov stability theory, backstepping technique and event-triggered control theory, an event-triggered protocol is proposed for the considered multiple mechanical systems. It is proved that the practical leader-following consensus can be achieved by the proposed protocol. Meanwhile, to exclude the Zeno behaviour, a positive lower bound of inter-event intervals is given. Finally, we provide a numerical simulation to illustrate the effectiveness of the given protocol.Dynamic attitude planning for trajectory tracking in thrust-vectoring UAVshttps://www.zbmath.org/1483.934402022-05-16T20:40:13.078697Z"Invernizzi, Davide"https://www.zbmath.org/authors/?q=ai:invernizzi.davide"Lovera, Marco"https://www.zbmath.org/authors/?q=ai:lovera.marco"Zaccarian, Luca"https://www.zbmath.org/authors/?q=ai:zaccarian.lucaEditorial remark: No review copy delivered.Distributed cooperative control for nonholonomic wheeled mobile robot systemshttps://www.zbmath.org/1483.934412022-05-16T20:40:13.078697Z"Kada, Belkacem"https://www.zbmath.org/authors/?q=ai:kada.belkacem"Balamesh, Ahmed S. A."https://www.zbmath.org/authors/?q=ai:balamesh.ahmed-s-a"Juhany, Khalid A."https://www.zbmath.org/authors/?q=ai:juhany.khalid-a"Al-Qadi, Ibraheem M."https://www.zbmath.org/authors/?q=ai:al-qadi.ibraheem-mSummary: The purpose of this paper is two-fold. First, the smoothness of the distributed consensus control (DCC) protocols of multi-agent systems (MAS) with inherent nonlinear dynamics is investigated. Different from the traditional consensus protocols where variable structure control is considered for robust control, a continuous DCC is presented to achieve consensus tracking without control chattering. Using certain types of exponential functions, it is shown that different smooth DCC schemes can be constructed to achieve asymptotic consensus tracking with smooth control input for MAS with connected directed/undirected and fixed/switched communication topologies. Second, the formation control problem of nonholonomic wheeled mobile robots (WMR) is solved via the continuous DCC. By converting the formation problem into consensus problem using the agents' kinematics, the formation speed-control problem in planar motion is formulated and solved. The translational and rotational speeds inputs to the WMR are computed using continuous distributed consensus protocols to reduce chattering in the control inputs of mobile robots. The distinctive feature of the proposed consensus and formation algorithms is the high tracking precision with smooth control input to agents' dynamics. In simulation studies, different numerical examples are illustrated to demonstrate the performance and effectiveness of the proposed DCC.Stable control strategy for a second-order nonholonomic planar underactuated mechanical systemhttps://www.zbmath.org/1483.934682022-05-16T20:40:13.078697Z"Lai, Xuzhi"https://www.zbmath.org/authors/?q=ai:lai.xuzhi"Xiong, Peiyin"https://www.zbmath.org/authors/?q=ai:xiong.peiyin"Wu, Min"https://www.zbmath.org/authors/?q=ai:wu.minSummary: This paper presents a stable control strategy for a planar four-link active-passive-active-active (APAA) underactuated mechanical system. The control objective is to move its end-point from any initial position to any target position. First, the controllers are designed to move the first link to the target angle which ensures the target position is within the reachable area of the planar three-link passive-active-active (PAA) system. Meantime, the system is reduced to a planar virtual pendubot. Then, the periodic controllers are designed based on the nilpotent approximation model to make the first link return to the target angle and all angular velocities converge to zeroes, where the fuzzy modulating is added to adjust the convergence of angular velocities. Thus, the system is reduced to a planar virtual PAA system. Next, the control is divided into two stages, and based on the angle constraint relationships, the target angles of the planar virtual PAA system for the target position are obtained by using the online particle swarm optimisation algorithm. Each stage controllers are designed according to the target angles, so the end-point of the planar APAA system is controlled to the target position. Finally, the validity of the control strategy is demonstrated via simulations.Stabilization of a class of nonlinear underactuated mechanical systems with 2-DOF via immersion and invariancehttps://www.zbmath.org/1483.934702022-05-16T20:40:13.078697Z"Romero, Jose Guadalupe"https://www.zbmath.org/authors/?q=ai:romero.jose-guadalupe"Gandarilla, Isaac"https://www.zbmath.org/authors/?q=ai:gandarilla.isaac"Santibáñez, Víctor"https://www.zbmath.org/authors/?q=ai:santibanez.victorSummary: In this work, we propose a controller based on the well-known immersion and invariance technique to solve the stabilization problem of a class of underactuated mechanical systems with 2-degree of freedom (DOF). We define simple conditions such that the ordinary partial equations arising in immersion and invariance are solved. The class of systems addressed in this work includes underactuated mechanical systems with \textit{gyroscopic forces}. Our approach is validated through simulation and experimental results.A new control method for global stabilisation of translational oscillator with rotational actuatorhttps://www.zbmath.org/1483.934762022-05-16T20:40:13.078697Z"Zhang, Ancai"https://www.zbmath.org/authors/?q=ai:zhang.ancai"She, Jinhua"https://www.zbmath.org/authors/?q=ai:she.jinhua"Qiu, Jianlong"https://www.zbmath.org/authors/?q=ai:qiu.jianlong"Yang, Chengdong"https://www.zbmath.org/authors/?q=ai:yang.chengdong"Alsaadi, Fawaz"https://www.zbmath.org/authors/?q=ai:alsaadi.fawaz-eSummary: A translational oscillator with a rotational actuator (TORA) is an underactuated mechanical system with two degrees of freedom. This paper presents a new method to solve the global stabilisation control problem for this underactuated system. First, a set of suitable state variables is chosen for the TORA. It transforms the system into a cascade affine nonlinear system. Then, a positive-definite Lyapunov function is constructed based on the structural characteristics of the system. A control law is designed to guarantee that the derivative of the Lyapunov function is non-positive. Finally, the global stability of the closed-loop control system is analysed using the LaSalle invariance principle. The condition on the control parameters is presented to globally stabilise the TORA at the origin. The effectiveness and robustness of the method are verified by a numerical example.Controlling the variable length pendulum: analysis and Lyapunov based design methodshttps://www.zbmath.org/1483.934852022-05-16T20:40:13.078697Z"Anderle, Milan"https://www.zbmath.org/authors/?q=ai:anderle.milan"Appeltans, Pieter"https://www.zbmath.org/authors/?q=ai:appeltans.pieter"Čelikovský, Sergej"https://www.zbmath.org/authors/?q=ai:celikovsky.sergej"Michiels, Wim"https://www.zbmath.org/authors/?q=ai:michiels.wim"Vyhlídal, Tomáš"https://www.zbmath.org/authors/?q=ai:vyhlidal.tomasSummary: The analysis and design of methods to damp the swing of the variable length pendulum by adjusting its length are presented here. To analyze the theoretical limits of such Coriolis force based damping, a comprehensive open-loop numerical analysis is performed for a two-dimensional model having the string length as the controlled input. Further, for a four dimensional model, having the force applied to the string as the controlled input, a smooth static state feedback controller is designed using backstepping. Results are verified both in simulations and through extensive laboratory experiments, and compared with previously published results achievable using an identical experimental setting.Angular velocity stabilization of underactuated rigid satellites based on energy shapinghttps://www.zbmath.org/1483.935002022-05-16T20:40:13.078697Z"Chen, Guanjun"https://www.zbmath.org/authors/?q=ai:chen.guanjun"Huo, Wei"https://www.zbmath.org/authors/?q=ai:huo.weiSummary: Angular velocity stabilization problem for underactuated rigid satellites with only two independent control inputs is investigated, and a novel stabilization control strategy based on energy shaping is presented in this paper. Firstly, a desired closed-loop system with a specific structure is constructed for the control objective. The matching condition and controller structure are determined by equating the underactuated satellite system with the desired system. Moreover, a feasible sufficient condition satisfying the matching condition is derived. By solving the sufficient condition according to three different structures of the satellite inertia tensor matrix, three nonlinear smooth stabilization control laws are obtained, and global asymptotic stability of the related closed-loop system is rigorously proved. Simulation results show effectiveness of the proposed control method.