Dragović, Vladimir; Gajić, Borislav; Jovanović, Božidar Gyroscopic Chaplygin systems and integrable magnetic flows on spheres. (English) Zbl 1517.37066 J. Nonlinear Sci. 33, No. 3, Paper No. 43, 51 p. (2023). MSC: 37J60 37J35 33E05 70E45 70E05 70F25 53Z05 PDFBibTeX XMLCite \textit{V. Dragović} et al., J. Nonlinear Sci. 33, No. 3, Paper No. 43, 51 p. (2023; Zbl 1517.37066) Full Text: DOI arXiv
Kalkan, Bahar; Li, Zijia; Schröcker, Hans-Peter; Siegele, Johannes The study variety of conformal kinematics. (English) Zbl 1503.70004 Adv. Appl. Clifford Algebr. 32, No. 4, Paper No. 44, 18 p. (2022). Reviewer: Niels Lubbes (Linz) MSC: 70E45 15A66 15A67 20G20 51B10 51F15 PDFBibTeX XMLCite \textit{B. Kalkan} et al., Adv. Appl. Clifford Algebr. 32, No. 4, Paper No. 44, 18 p. (2022; Zbl 1503.70004) Full Text: DOI arXiv
Ratiu, Tudor S.; Tarama, Daisuke Geodesic flows on real forms of complex semi-simple Lie groups of rigid body type. (English) Zbl 1460.53074 Res. Math. Sci. 7, No. 4, Paper No. 32, 36 p. (2020). Reviewer: Miguel Paternain (Montevideo) MSC: 53D25 70E15 70E45 22E46 PDFBibTeX XMLCite \textit{T. S. Ratiu} and \textit{D. Tarama}, Res. Math. Sci. 7, No. 4, Paper No. 32, 36 p. (2020; Zbl 1460.53074) Full Text: DOI
Buzzi, Claudio A.; Llibre, Jaume; Pazim, Rubens On the dynamics of the Euler equations on so(4). (English) Zbl 1447.37057 Dyn. Syst. 35, No. 2, 361-368 (2020). MSC: 37J35 70E15 70E40 70E45 PDFBibTeX XMLCite \textit{C. A. Buzzi} et al., Dyn. Syst. 35, No. 2, 361--368 (2020; Zbl 1447.37057) Full Text: DOI Link
Kibkalo, Vladislav Topological classification of Liouville foliations for the Kovalevskaya integrable case on the Lie algebra \(\operatorname{so}(3, 1)\). (English) Zbl 1439.37061 Topology Appl. 275, Article ID 107028, 10 p. (2020). Reviewer: William J. Satzer Jr. (St. Paul) MSC: 37J39 37J35 37J20 70E40 70E45 PDFBibTeX XMLCite \textit{V. Kibkalo}, Topology Appl. 275, Article ID 107028, 10 p. (2020; Zbl 1439.37061) Full Text: DOI arXiv
García-Naranjo, Luis C. Generalisation of Chaplygin’s reducing multiplier theorem with an application to multi-dimensional nonholonomic dynamics. (English) Zbl 1509.37077 J. Phys. A, Math. Theor. 52, No. 20, Article ID 205203, 16 p. (2019). MSC: 37J60 70E18 70E45 PDFBibTeX XMLCite \textit{L. C. García-Naranjo}, J. Phys. A, Math. Theor. 52, No. 20, Article ID 205203, 16 p. (2019; Zbl 1509.37077) Full Text: DOI arXiv
García-Naranjo, Luis C. Hamiltonisation, measure preservation and first integrals of the multi-dimensional rubber Routh sphere. (English) Zbl 1474.37077 Theor. Appl. Mech. (Belgrade) 46, No. 1, 65-88 (2019). MSC: 37J60 70E45 PDFBibTeX XMLCite \textit{L. C. García-Naranjo}, Theor. Appl. Mech. (Belgrade) 46, No. 1, 65--88 (2019; Zbl 1474.37077) Full Text: DOI arXiv
Qi, Guoyuan Modelings and mechanism analysis underlying both the 4D Euler equations and Hamiltonian conservative chaotic systems. (English) Zbl 1432.70020 Nonlinear Dyn. 95, No. 3, 2063-2077 (2019). MSC: 70E45 70E20 70E40 PDFBibTeX XMLCite \textit{G. Qi}, Nonlinear Dyn. 95, No. 3, 2063--2077 (2019; Zbl 1432.70020) Full Text: DOI
Fomenko, A. T.; Vedyushkina, V. V. Implementation of integrable systems by topological, geodesic billiards with potential and magnetic field. (English) Zbl 1459.37044 Russ. J. Math. Phys. 26, No. 3, 320-333 (2019). MSC: 37J35 37J39 37C83 70E40 70E45 PDFBibTeX XMLCite \textit{A. T. Fomenko} and \textit{V. V. Vedyushkina}, Russ. J. Math. Phys. 26, No. 3, 320--333 (2019; Zbl 1459.37044) Full Text: DOI
Fassò, Francesco; García-Naranjo, Luis C.; Montaldi, James Integrability and dynamics of the \(n\)-dimensional symmetric Veselova top. (English) Zbl 1418.37107 J. Nonlinear Sci. 29, No. 3, 1205-1246 (2019). MSC: 37J60 70E17 70E40 70E45 70F25 70K43 PDFBibTeX XMLCite \textit{F. Fassò} et al., J. Nonlinear Sci. 29, No. 3, 1205--1246 (2019; Zbl 1418.37107) Full Text: DOI arXiv
Shamolin, M. V. A new case of an integrable system with dissipation on the tangent bundle of a multidimensional sphere. (English. Russian original) Zbl 1397.70009 Mosc. Univ. Mech. Bull. 73, No. 3, 51-59 (2018); translation from Vestn. Mosk. Univ., Ser. I 73, No. 3, 34-43 (2018). MSC: 70E17 70E45 70G60 PDFBibTeX XMLCite \textit{M. V. Shamolin}, Mosc. Univ. Mech. Bull. 73, No. 3, 51--59 (2018; Zbl 1397.70009); translation from Vestn. Mosk. Univ., Ser. I 73, No. 3, 34--43 (2018) Full Text: DOI
Shamolin, M. V. Integrable variable dissipation systems on the tangent bundle of a multi-dimensional sphere and some applications. (English. Russian original) Zbl 1416.70009 J. Math. Sci., New York 230, No. 2, 185-353 (2018); translation from Fundam. Prikl. Mat. 20, No. 4, 3-231 (2015). Reviewer: Vladimir Sobolev (Samara) MSC: 70E45 70E40 37J05 PDFBibTeX XMLCite \textit{M. V. Shamolin}, J. Math. Sci., New York 230, No. 2, 185--353 (2018; Zbl 1416.70009); translation from Fundam. Prikl. Mat. 20, No. 4, 3--231 (2015) Full Text: DOI
Shamolin, M. V. The case of integrable systems with dissipation on the tangent bundle of a multidimensional sphere. (English. Russian original) Zbl 1404.37071 J. Math. Sci., New York 228, No. 6, 723-730 (2018); translation from Probl. Mat. Anal. 90, 107-113 (2018). Reviewer: Teodor Atanacković (Novi Sad) MSC: 37J35 70E40 70E45 PDFBibTeX XMLCite \textit{M. V. Shamolin}, J. Math. Sci., New York 228, No. 6, 723--730 (2018; Zbl 1404.37071); translation from Probl. Mat. Anal. 90, 107--113 (2018) Full Text: DOI
Qiao, Hui Multiple forced rotational solutions for the planar \(N\)-pendulum equation. (English) Zbl 1382.37064 Acta Math. Sin., Engl. Ser. 34, No. 2, 171-193 (2018). MSC: 37J45 34C25 58E05 37N05 70E45 PDFBibTeX XMLCite \textit{H. Qiao}, Acta Math. Sin., Engl. Ser. 34, No. 2, 171--193 (2018; Zbl 1382.37064) Full Text: DOI
Shamolin, M. V. Cases of integrability corresponding to the pendulum motion in four-dimensional space. (Russian. English summary) Zbl 1393.70017 Vestn. Samar. Univ., Estestvennonauchn. Ser. 23, No. 1, 41-58 (2017). MSC: 70E45 PDFBibTeX XMLCite \textit{M. V. Shamolin}, Vestn. Samar. Univ., Estestvennonauchn. Ser. 23, No. 1, 41--58 (2017; Zbl 1393.70017) Full Text: MNR
Gajić, Borislav; Dragović, Vladimir; Jovanović, Božidar On the completeness of the Manakov integrals. (English. Russian original) Zbl 1404.37068 J. Math. Sci., New York 223, No. 6, 675-685 (2017); translation from Fundam. Prikl. Mat. 20, No. 2, 35-49 (2015). Reviewer: Teodor Atanacković (Novi Sad) MSC: 37J35 70E40 70E45 70E17 PDFBibTeX XMLCite \textit{B. Gajić} et al., J. Math. Sci., New York 223, No. 6, 675--685 (2017; Zbl 1404.37068); translation from Fundam. Prikl. Mat. 20, No. 2, 35--49 (2015) Full Text: DOI arXiv
Shamolin, M. V. New cases of integrability of equations of motion of a rigid body in the \(n\)-dimensional space. (English. Russian original) Zbl 1412.70009 J. Math. Sci., New York 221, No. 2, 205-259 (2017); translation from Sovrem. Mat. Prilozh. 98 (2015). MSC: 70E40 70E45 70H06 37J35 37N05 PDFBibTeX XMLCite \textit{M. V. Shamolin}, J. Math. Sci., New York 221, No. 2, 205--259 (2017; Zbl 1412.70009); translation from Sovrem. Mat. Prilozh. 98 (2015) Full Text: DOI
Dragović, Vladimir; Gajić, Borislav Some recent generalizations of the classical rigid body systems. (English) Zbl 1378.70007 Arnold Math. J. 2, No. 4, 511-578 (2016). MSC: 70E40 70E17 70E45 70H06 14H70 PDFBibTeX XMLCite \textit{V. Dragović} and \textit{B. Gajić}, Arnold Math. J. 2, No. 4, 511--578 (2016; Zbl 1378.70007) Full Text: DOI
Bizyaev, I. A.; Kozlov, V. V. Homogeneous systems with quadratic integrals, Lie-Poisson quasibrackets, and Kovalevskaya’s method. (English) Zbl 1358.37099 Sb. Math. 206, No. 12, 1682-1706 (2015); translation from Mat. Sb. 206, No. 12, 29-54 (2015). MSC: 37J35 37J05 37J30 70E45 70H05 70H06 70H07 PDFBibTeX XMLCite \textit{I. A. Bizyaev} and \textit{V. V. Kozlov}, Sb. Math. 206, No. 12, 1682--1706 (2015; Zbl 1358.37099); translation from Mat. Sb. 206, No. 12, 29--54 (2015) Full Text: DOI
Shamolin, M. V. Classification of integrable cases in the dynamics of a four-dimensional rigid body in a nonconservative field in the presence of a tracking force. (English. Russian original) Zbl 1346.70007 J. Math. Sci., New York 204, No. 6, 808-870 (2015); translation from Sovrem. Mat. Prilozh. 88 (2013). Reviewer: Teodor Atanacković (Novi Sad) MSC: 70E45 70E40 PDFBibTeX XMLCite \textit{M. V. Shamolin}, J. Math. Sci., New York 204, No. 6, 808--870 (2015; Zbl 1346.70007); translation from Sovrem. Mat. Prilozh. 88 (2013) Full Text: DOI
Shamolin, M. V. Some classes of integrable problems in spatial dynamics of a rigid body in a nonconservative force field. (English. Russian original) Zbl 1353.70020 J. Math. Sci., New York 210, No. 3, 292-330 (2015); translation from Tr. Semin. Im. I. G. Petrovskogo 30, No. 2, 287-350 (2014). MSC: 70E40 70E45 70H06 17B80 37J35 PDFBibTeX XMLCite \textit{M. V. Shamolin}, J. Math. Sci., New York 210, No. 3, 292--330 (2015; Zbl 1353.70020); translation from Tr. Semin. Im. I. G. Petrovskogo 30, No. 2, 287--350 (2014) Full Text: DOI
Dragović, Vladimir; Gajić, Borislav; Jovanović, Božidar Note on free symmetric rigid body motion. (English) Zbl 1351.37225 Regul. Chaotic Dyn. 20, No. 3, 293-308 (2015). Reviewer: Cristian Lăzureanu (Timisoara) MSC: 37J35 70H06 70E45 PDFBibTeX XMLCite \textit{V. Dragović} et al., Regul. Chaotic Dyn. 20, No. 3, 293--308 (2015; Zbl 1351.37225) Full Text: DOI
Ratiu, Tudor S.; Tarama, Daisuke The \(U(n)\) free rigid body: integrability and stability analysis of the equilibria. (English) Zbl 1378.70005 J. Differ. Equations 259, No. 12, 7284-7331 (2015). MSC: 70E15 70E45 34D20 37K10 70H06 PDFBibTeX XMLCite \textit{T. S. Ratiu} and \textit{D. Tarama}, J. Differ. Equations 259, No. 12, 7284--7331 (2015; Zbl 1378.70005) Full Text: DOI
Shamolin, M. V. Variety of integrable cases in dynamics of low- and multi-dimensional rigid bodies in nonconservative force fields. (English. Russian original) Zbl 1353.70019 J. Math. Sci., New York 204, No. 4, 379-530 (2015); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 125, 5-254 (2013). MSC: 70E40 37J35 37N05 70-02 37-02 70E18 70E45 PDFBibTeX XMLCite \textit{M. V. Shamolin}, J. Math. Sci., New York 204, No. 4, 379--530 (2015; Zbl 1353.70019); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 125, 5--254 (2013) Full Text: DOI
Dragović, Vladimir; Gajić, Borislav Four-dimensional generalization of the Grioli precession. (English) Zbl 1353.70024 Regul. Chaotic Dyn. 19, No. 6, 656-662 (2014). MSC: 70E45 70E17 PDFBibTeX XMLCite \textit{V. Dragović} and \textit{B. Gajić}, Regul. Chaotic Dyn. 19, No. 6, 656--662 (2014; Zbl 1353.70024) Full Text: DOI
Shamolin, Maxim V. Variety of the cases of integrability in dynamics of a symmetric 2d-, 3d- and 4d-rigid body in a nonconservative field. (English) Zbl 1359.70059 Int. J. Struct. Stab. Dyn. 13, No. 7, Article ID 1340011, 14 p. (2013). MSC: 70E40 70E18 70E45 PDFBibTeX XMLCite \textit{M. V. Shamolin}, Int. J. Struct. Stab. Dyn. 13, No. 7, Article ID 1340011, 14 p. (2013; Zbl 1359.70059) Full Text: DOI
Gajić, Borislav The rigid body dynamics: classical and algebro-geometric integration. (English) Zbl 1313.70001 Dragović, Vladimir (ed.) et al., Mechanics, integrability and control. Beograd: Matematički Institut SANU (ISBN 978-86-80593-48-7). Zbornik Radova (Beograd) 16(24), 5-44 (2013). Reviewer: Božidar Jovanović (Beograd) MSC: 70-02 70E17 70E40 70E45 PDFBibTeX XMLCite \textit{B. Gajić}, Zb. Rad. (Beogr.) 16, 5--44 (2013; Zbl 1313.70001) Full Text: arXiv
Chenciner, Alain; Jiménez-Pérez, Hugo Angular momentum and Horn’s problem. (English) Zbl 1366.70015 Mosc. Math. J. 13, No. 4, 621-630 (2013). MSC: 70F10 70E45 15A18 PDFBibTeX XMLCite \textit{A. Chenciner} and \textit{H. Jiménez-Pérez}, Mosc. Math. J. 13, No. 4, 621--630 (2013; Zbl 1366.70015) Full Text: arXiv Link
Shamolin, M. V. New case of integrability of dynamic equations on the tangent bundle of a 3-sphere. (English. Russian original) Zbl 1356.70011 Russ. Math. Surv. 68, No. 5, 963-965 (2013); translation from Usp. Mat. Nauk 68, No. 5, 185-186 (2013). Reviewer: Teodor Atanacković (Novi Sad) MSC: 70E40 70E45 PDFBibTeX XMLCite \textit{M. V. Shamolin}, Russ. Math. Surv. 68, No. 5, 963--965 (2013; Zbl 1356.70011); translation from Usp. Mat. Nauk 68, No. 5, 185--186 (2013) Full Text: DOI MNR
Izosimov, A. M. Stability of stationary rotations of multidimensional rigid body. (English. Russian original) Zbl 1268.70007 Mosc. Univ. Math. Bull. 68, No. 1, 80-82 (2013); translation from Vestn. Mosk. Univ., Ser. I 68, No. 1, 59-62 (2013). MSC: 70E50 70E15 70E45 PDFBibTeX XMLCite \textit{A. M. Izosimov}, Mosc. Univ. Math. Bull. 68, No. 1, 80--82 (2013; Zbl 1268.70007); translation from Vestn. Mosk. Univ., Ser. I 68, No. 1, 59--62 (2013) Full Text: DOI
Arthamonov, S. B. New integrable systems as a limit of the elliptic \(SL(N,\mathbb C)\) top. (English. Russian original) Zbl 1417.37197 Theor. Math. Phys. 171, No. 2, 589-599 (2012); translation from Teor. Mat. Fiz. 171, No. 2, 196-207 (2012). MSC: 37J35 70E40 70E45 70G65 PDFBibTeX XMLCite \textit{S. B. Arthamonov}, Theor. Math. Phys. 171, No. 2, 589--599 (2012; Zbl 1417.37197); translation from Teor. Mat. Fiz. 171, No. 2, 196--207 (2012) Full Text: DOI
Aminov, G. A. Limit relation between Toda chains and the elliptic \(\mathrm{SL}(N,\mathbb{C})\) top. (English. Russian original) Zbl 1417.37196 Theor. Math. Phys. 171, No. 2, 575-588 (2012); translation from Teor. Mat. Fiz. 171, No. 2, 179-195 (2012). MSC: 37J35 34M56 70E40 70E45 70G65 PDFBibTeX XMLCite \textit{G. A. Aminov}, Theor. Math. Phys. 171, No. 2, 575--588 (2012; Zbl 1417.37196); translation from Teor. Mat. Fiz. 171, No. 2, 179--195 (2012) Full Text: DOI
Georgievskii, D. V.; Shamolin, M. V. Levi-Civita symbols, generalized vector products, and new integrable cases in mechanics of multidimensional bodies. (English. Russian original) Zbl 1278.70007 J. Math. Sci., New York 187, No. 3, 280-299 (2012); translation from Sovrem. Mat. Prilozh. 76 (2012). Reviewer: Nenad Manojlović (Faro) MSC: 70E40 70E45 37J35 PDFBibTeX XMLCite \textit{D. V. Georgievskii} and \textit{M. V. Shamolin}, J. Math. Sci., New York 187, No. 3, 280--299 (2012; Zbl 1278.70007); translation from Sovrem. Mat. Prilozh. 76 (2012) Full Text: DOI
Dragović, Vladimir; Gajić, Borislav On the cases of Kirchhoff and Chaplygin of the Kirchhoff equations. (English) Zbl 1252.70022 Regul. Chaotic Dyn. 17, No. 5, 431-438 (2012). MSC: 70E40 70E45 70E20 PDFBibTeX XMLCite \textit{V. Dragović} and \textit{B. Gajić}, Regul. Chaotic Dyn. 17, No. 5, 431--438 (2012; Zbl 1252.70022) Full Text: DOI arXiv
Birtea, Petre; Caşu, Ioan; Ratiu, Tudor S.; Turhan, Murat Stability of equilibria for the \(\mathfrak{so}(4)\) free rigid body. (English) Zbl 1300.70005 J. Nonlinear Sci. 22, No. 2, 187-212 (2012). MSC: 70E17 70E45 70G45 70K20 PDFBibTeX XMLCite \textit{P. Birtea} et al., J. Nonlinear Sci. 22, No. 2, 187--212 (2012; Zbl 1300.70005) Full Text: DOI arXiv
Belyaev, A. V. Asymptotic behaviour of singular points of solutions of the problem of heavy \(n\)-dimensional body motion in the Lagrange case. (English. Russian original) Zbl 1367.70011 Sb. Math. 202, No. 11, 1617-1635 (2011); translation from Mat. Sb. 202, No. 11, 55-74 (2011). MSC: 70E45 34C05 PDFBibTeX XMLCite \textit{A. V. Belyaev}, Sb. Math. 202, No. 11, 1617--1635 (2011; Zbl 1367.70011); translation from Mat. Sb. 202, No. 11, 55--74 (2011) Full Text: DOI
Novikov, D. V. Topological features of the Sokolov integrable case on the Lie algebra \( \mathrm{e}(3)\). (English) Zbl 1246.37081 Sb. Math. 202, No. 5, 749 (2011); translation from Mat. Sb. 202, No. 5, 127-160 (2011). Reviewer: Ivailo Mladenov (Sofia) MSC: 37J35 37J15 70E40 70E45 PDFBibTeX XMLCite \textit{D. V. Novikov}, Sb. Math. 202, No. 5, 749 (2011; Zbl 1246.37081); translation from Mat. Sb. 202, No. 5, 127--160 (2011) Full Text: DOI
Escher, J.; Kohlmann, M.; Lenells, J. The geometry of the two-component Camassa-Holm and Degasperis-Procesi equations. (English) Zbl 1210.58007 J. Geom. Phys. 61, No. 2, 436-452 (2011). MSC: 58D05 70E45 PDFBibTeX XMLCite \textit{J. Escher} et al., J. Geom. Phys. 61, No. 2, 436--452 (2011; Zbl 1210.58007) Full Text: DOI arXiv
Aminov, G.; Arthamonov, S. Reduction of the elliptic \(\mathrm{SL}(N,\mathbb C)\) top. (English) Zbl 1252.37048 J. Phys. A, Math. Theor. 44, No. 7, Article ID 075201, 34 p. (2011). MSC: 37J35 70E40 70E45 70H06 PDFBibTeX XMLCite \textit{G. Aminov} and \textit{S. Arthamonov}, J. Phys. A, Math. Theor. 44, No. 7, Article ID 075201, 34 p. (2011; Zbl 1252.37048) Full Text: DOI arXiv
Casu, Ioan WITHDRAWN: On the stability problem and a bifurcation phenomenon for a special class of equilibria of the free rigid body on \(\mathfrak{so}(5)\). arXiv:1103.5583 Preprint, arXiv:1103.5583 [math.DS] (2011); retraction notice ibid. MSC: 34D20 70E17 70E45 BibTeX Cite \textit{I. Casu}, ``WITHDRAWN: On the stability problem and a bifurcation phenomenon for a special class of equilibria of the free rigid body on $\mathfrak{so}(5)$'', Preprint, arXiv:1103.5583 [math.DS] (2011); retraction notice ibid. Full Text: arXiv OA License
Shamolin, M. V. Classification of complete integrability cases in four-dimensional symmetric rigid-body dynamics in a nonconservative field. (English. Russian original) Zbl 1288.70001 J. Math. Sci., New York 165, No. 6, 743-754 (2010); translation from Sovrem. Mat. Prilozh. 65, 1311-141 (2009). MSC: 70E45 70E15 70H06 PDFBibTeX XMLCite \textit{M. V. Shamolin}, J. Math. Sci., New York 165, No. 6, 743--754 (2010; Zbl 1288.70001); translation from Sovrem. Mat. Prilozh. 65, 1311--141 (2009) Full Text: DOI
Shamolin, M. V. The case of complete integrability in the dynamics of a four-dimensional rigid body in a nonconservative field. (English. Russian original) Zbl 1356.70010 Russ. Math. Surv. 65, No. 1, 183-185 (2010); translation from Usp. Mat. Nauk. 65, No. 1, 189-190 (2010). Reviewer: Teodor Atanacković (Novi Sad) MSC: 70E40 70E45 PDFBibTeX XMLCite \textit{M. V. Shamolin}, Russ. Math. Surv. 65, No. 1, 183--185 (2010; Zbl 1356.70010); translation from Usp. Mat. Nauk. 65, No. 1, 189--190 (2010) Full Text: DOI MNR
Sinitsyn, Evguenii; Zhilinskii, Boris Qualitative analysis of the classical and quantum Manakov top. (English) Zbl 1139.81060 SIGMA, Symmetry Integrability Geom. Methods Appl. 3, Paper 046, 23 p. (2007). Reviewer: Piotr Garbaczewski (Opole) MSC: 81V55 70E99 70E45 70H05 81R12 PDFBibTeX XMLCite \textit{E. Sinitsyn} and \textit{B. Zhilinskii}, SIGMA, Symmetry Integrability Geom. Methods Appl. 3, Paper 046, 23 p. (2007; Zbl 1139.81060) Full Text: DOI arXiv EuDML EMIS
Gorr, G. V.; Shchetinina, E. K. On the integrating multiplier of equations of dynamics of a solid body on invariant manifolds. (Russian. English summary) Zbl 1126.70316 Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2007, No. 1, 60-66 (2007). MSC: 70E45 PDFBibTeX XMLCite \textit{G. V. Gorr} and \textit{E. K. Shchetinina}, Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2007, No. 1, 60--66 (2007; Zbl 1126.70316)
Sinclair, Andrew J.; Hurtado, John E. Cayley kinematics and the Cayley form of dynamic equations. (English) Zbl 1145.70301 Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 461, No. 2055, 761-781 (2005). MSC: 70B10 70E15 70E45 PDFBibTeX XMLCite \textit{A. J. Sinclair} and \textit{J. E. Hurtado}, Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 461, No. 2055, 761--781 (2005; Zbl 1145.70301) Full Text: DOI
Perelomov, A. M. Motion of four-dimensional rigid body around a fixed point: an elementary approach. I. (English) Zbl 1078.70007 J. Phys. A, Math. Gen. 38, No. 47, L801-L807 (2005). MSC: 70E17 70E45 PDFBibTeX XMLCite \textit{A. M. Perelomov}, J. Phys. A, Math. Gen. 38, No. 47, L801--L807 (2005; Zbl 1078.70007) Full Text: DOI arXiv
Gołubowska, Barbara Action-angle analysis of some geometric models of internal degrees of freedom. (English) Zbl 1362.70004 J. Nonlinear Math. Phys. 11, Suppl. 1, 138-144 (2004). MSC: 70E05 70E17 70E45 PDFBibTeX XMLCite \textit{B. Gołubowska}, J. Nonlinear Math. Phys. 11, 138--144 (2004; Zbl 1362.70004) Full Text: DOI
Tsiganov, A. V. Integrable deformations of tops related to the algebra \(\mathrm{so}(p,q)\). (English) Zbl 1178.70070 Theor. Math. Phys. 141, No. 1, 1348-1360 (2004); translation from Teor. Mat. Fiz. 141, No. 1, 24-37 (2004). MSC: 70E40 37J35 70E45 PDFBibTeX XMLCite \textit{A. V. Tsiganov}, Theor. Math. Phys. 141, No. 1, 1348--1360 (2004; Zbl 1178.70070); translation from Teor. Mat. Fiz. 141, No. 1, 24--37 (2004) Full Text: DOI
Golubchik, I. Z.; Sokolov, V. V. Factorization of the loop algebra and integrable toplike systems. (English) Zbl 1178.37075 Theor. Math. Phys. 141, No. 1, 1329-1347 (2004); translation from Teor. Mat. Fiz. 141, No. 1, 3-23 (2004). MSC: 37K10 37K30 70E45 PDFBibTeX XMLCite \textit{I. Z. Golubchik} and \textit{V. V. Sokolov}, Theor. Math. Phys. 141, No. 1, 1329--1347 (2004; Zbl 1178.37075); translation from Teor. Mat. Fiz. 141, No. 1, 3--23 (2004) Full Text: DOI arXiv
Bruschi, M.; Calogero, F. Convenient parameterizations of matrices in terms of vectors. (English) Zbl 1138.15301 Phys. Lett., A 327, No. 4, 312-319 (2004). MSC: 15A90 70E45 70F10 PDFBibTeX XMLCite \textit{M. Bruschi} and \textit{F. Calogero}, Phys. Lett., A 327, No. 4, 312--319 (2004; Zbl 1138.15301) Full Text: DOI arXiv
Dragović, Vladimir; Gajić, Borislav The Lagrange bitop on \(\text{so}(4)\times \text{so}(4)\) and geometry of the Prym varieties. (English) Zbl 1125.37316 Am. J. Math. 126, No. 5, 981-1004 (2004). MSC: 37J35 14H40 70E45 70G55 70E40 PDFBibTeX XMLCite \textit{V. Dragović} and \textit{B. Gajić}, Am. J. Math. 126, No. 5, 981--1004 (2004; Zbl 1125.37316) Full Text: DOI arXiv Link
Dragović, Vladimir On integrability and rigid-body systems. (English) Zbl 1289.37033 Dragovich, B.(ed.) et al., Proceedings of the 2nd summer school in modern mathematical physics, Kopaonik, Yugoslavia, September 1–12, 2002. Belgrade: Institute of Physics (ISBN 86-82441-13-6). Sveske Fizičkikh Nauka. Series A: Conferences 16, 1, 533-548 (2003). Reviewer: Borislav Gajić (Beograd) MSC: 37J35 14H70 70E45 PDFBibTeX XMLCite \textit{V. Dragović}, in: Proceedings of the 2nd summer school in modern mathematical physics, Kopaonik, Yugoslavia, September 1--12, 2002. Belgrade: Institute of Physics. 533--548 (2003; Zbl 1289.37033)
Borisov, A. V.; Mamaev, I. S. Modern methods in the theory of integrable systems. Bi-Hamiltonian description, Lax representation, and separation of variables. (Современные методы теории интегрируемых систем. Бигамильтоново описание, представление Лакса, разделение переменных.) (Russian) Zbl 1101.37041 Sovremennaya Matematika. Izhevsk: Institut Komp’yuternykh Issledovaniĭ (ISBN 5-93972-219-9/hbk). 295 p. (2003). Reviewer: Boris V. Loginov (Ul’yanovsk) MSC: 37-02 70-02 37J35 37K05 37K10 70H06 70E45 PDFBibTeX XMLCite \textit{A. V. Borisov} and \textit{I. S. Mamaev}, Современные методы теории интегрируемых систем. Бигамильтоново описание, представление Лакса, разделение переменных (Russian). Izhevsk: Institut Komp'yuternykh Issledovanij (2003; Zbl 1101.37041)
Sławianowski, Jan J.; Kovalchuk, Vasyl Invariant geodetic problems on the affine group and related Hamiltonian systems. (English) Zbl 1047.37056 Rep. Math. Phys. 51, No. 2-3, 371-379 (2003). Reviewer: Mircea Crâşmăreanu (Iaşi) MSC: 37N05 70E45 37J05 22E70 53C22 70H03 70H05 70H33 PDFBibTeX XMLCite \textit{J. J. Sławianowski} and \textit{V. Kovalchuk}, Rep. Math. Phys. 51, No. 2--3, 371--379 (2003; Zbl 1047.37056) Full Text: DOI
Akulenko, L. D.; Smatkov, A. M. On the quickest hit on a sphere with zero velocity. (Russian) Zbl 1075.70543 Dokl. Akad. Nauk, Ross. Akad. Nauk 379, No. 1, 28-32 (2001). Reviewer: Andrei Zemskov (Moskva) MSC: 70Q05 70E45 PDFBibTeX XMLCite \textit{L. D. Akulenko} and \textit{A. M. Smatkov}, Dokl. Akad. Nauk, Ross. Akad. Nauk 379, No. 1, 28--32 (2001; Zbl 1075.70543)
Ballard, Patrick Formulation and well-posedness of the dynamics of rigid-body systems with perfect unilateral constraints. (English) Zbl 1014.70005 Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 359, No. 1789, 2327-2346 (2001). MSC: 70E55 70F35 70E45 70F25 PDFBibTeX XMLCite \textit{P. Ballard}, Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 359, No. 1789, 2327--2346 (2001; Zbl 1014.70005) Full Text: DOI HAL
Jank, W. Special shaky and overclosed mechanisms. (Spezielle wackelige and übergeschlossene Mechanismen.) (German) Zbl 0963.70518 Röschel, O. (ed.) et al., Geometrie-Tagung “107 Jahre Drehfluchtprinzip”, Vorau, Österreich, 1. Juni-6. Juni 1997. Tagungsband. Vorau: TU Graz, 94 (1999). MSC: 70B15 70E45 52C25 PDFBibTeX XMLCite \textit{W. Jank}, in: Geometrie-Tagung ``107 Jahre Drehfluchtprinzip'', Vorau, Österreich, 1. Juni--6. Juni 1997. Tagungsband. Vorau: TU Graz. 94 (1999; Zbl 0963.70518)
Fairlie, David B.; Ueno, Tatsuya Higher-dimensional generalisations of the Euler top equations. (English) Zbl 0945.70508 Phys. Lett., A 240, No. 3, 132-136 (1998). MSC: 70E45 70E40 PDFBibTeX XMLCite \textit{D. B. Fairlie} and \textit{T. Ueno}, Phys. Lett., A 240, No. 3, 132--136 (1998; Zbl 0945.70508) Full Text: DOI arXiv
Bolsinov, A. V. Multidimensional Euler and Clebsch cases and Lie pencils. (English) Zbl 0985.37063 Fomenko, A. T. (ed.) et al., Tensor and vector analysis. Geometry, mechanics and physics. Reading: Gordon and Breach Science Publishers. 25-30 (1998). MSC: 37J35 70E45 37J05 70H06 PDFBibTeX XMLCite \textit{A. V. Bolsinov}, in: Tensor and vector analysis. Geometry, mechanics and physics. Reading: Gordon and Breach Science Publishers. 25--30 (1998; Zbl 0985.37063)
Borisov, A. V.; Mamaev, I. S. Nonlinear Poisson brackets and isomorphisms in dynamics. (Russian. English summary) Zbl 0954.37032 Regul. Khaoticheskaya Din. 2, No. 3-4, 72-89 (1997). MSC: 37J35 70H07 70E40 70E45 PDFBibTeX XMLCite \textit{A. V. Borisov} and \textit{I. S. Mamaev}, Regul. Khaoticheskaya Din. 2, No. 3--4, 72--89 (1997; Zbl 0954.37032)
Fedorov, Yu. Integrable systems, Poisson pencils, and hyperelliptic Lax pairs. (English. Russian original) Zbl 0985.37060 J. Math. Sci., New York 94, No. 4, 1501-1511 (1999); translation from Zap. Nauchn. Semin. POMI 235, 87-103 (1996). MSC: 37J35 37N05 70H06 70E40 70E45 PDFBibTeX XMLCite \textit{Yu. Fedorov}, J. Math. Sci., New York 94, No. 4, 1 (1996; Zbl 0985.37060); translation from Zap. Nauchn. Semin. POMI 235, 87--103 (1996) Full Text: DOI EuDML
Fedorov, Yu. N. A generalized Poinsot interpretation of the motion of a multidimensional rigid body. (English. Russian original) Zbl 0963.70525 Proc. Steklov Inst. Math. 205, 181-186 (1995); translation from Tr. Mat. Inst. Steklova 205, 200-206 (1994). MSC: 70E45 70E05 PDFBibTeX XMLCite \textit{Yu. N. Fedorov}, in: New results in the theory of topological classification of integrable systems. Providence, RI: American Mathematical Society. 1 (1994; Zbl 0963.70525); translation from Tr. Mat. Inst. Steklova 205, 200--206 (1994)