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Found 107 Documents (Results 1–100)

Motion of a rigid body with frontal cone in a resistive medium: qualitative analysis and integrability. (English. Russian original) Zbl 1524.70048

J. Math. Sci., New York 272, No. 5, 703-728 (2023); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 174, 83-108 (2020).
MSC:  70G60
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Dissipative systems: relative roughness, nonroughness of various degrees, and integrability. (English. Russian original) Zbl 1524.70047

J. Math. Sci., New York 272, No. 5, 690-702 (2023); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 174, 70-82 (2020).
MSC:  70G60 37N05
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Odd-order integrable dynamical systems with dissipation. (English. Russian original) Zbl 1519.70016

J. Math. Sci., New York 272, No. 5, 672-689 (2023); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 174, 52-69 (2020).
MSC:  70G60 70H06 37J35
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New cases of homogeneous integrable systems with dissipation on tangent bundles of four-dimensional manifolds. (English. Russian original) Zbl 1482.37059

Dokl. Math. 103, No. 2, 85-91 (2021); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 497, 23-30 (2021).
MSC:  37J35 37J39 70H06
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Diagnostic problem for a model of a gyrostabilized platform. (English. Russian original) Zbl 1473.70010

J. Math. Sci., New York 257, No. 1, 138-142 (2021); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 160, 137-141 (2019).
MSC:  70E05
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New cases of homogeneous integrable systems with dissipation on tangent bundles of three-dimensional manifolds. (English. Russian original) Zbl 1482.37058

Dokl. Math. 102, No. 3, 518-523 (2020); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 495, 84-90 (2020).
MSC:  37J35 37J39 70H06
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New cases of homogeneous integrable systems with dissipation on tangent bundles of two-dimensional manifolds. (English. Russian original) Zbl 1482.37057

Dokl. Math. 102, No. 2, 443-448 (2020); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 494, 105-111 (2020).
MSC:  37J35 37J39 70H06
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Problems of qualitative analysis in the spatial dynamics of rigid bodies interacting with media. (English. Russian original) Zbl 1471.70015

J. Math. Sci., New York 250, No. 6, 984-996 (2020); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 150, 130-142 (2018).
MSC:  70G60
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Examples of integrable systems with dissipation on the tangent bundles of four-dimensional manifolds. (English. Russian original) Zbl 1471.70014

J. Math. Sci., New York 250, No. 6, 973-983 (2020); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 150, 119-129 (2018).
MSC:  70G60
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Examples of integrable systems with dissipation on the tangent bundles of three-dimensional manifolds. (English. Russian original) Zbl 1471.70013

J. Math. Sci., New York 250, No. 6, 964-972 (2020); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 150, 110-118 (2018).
MSC:  70G60
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Examples of integrable systems with dissipation on the tangent bundles of multidimensional spheres. (English. Russian original) Zbl 1471.70012

J. Math. Sci., New York 250, No. 6, 932-941 (2020); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 150, 78-87 (2018).
MSC:  70G60
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Integrable systems with dissipation on the tangent bundles of 2- and 3-dimensional spheres. (English. Russian original) Zbl 1455.70010

J. Math. Sci., New York 245, No. 4, 498-507 (2020); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 145, 86-94 (2018).
MSC:  70G60
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New examples of integrable systems with dissipation on the tangent bundles of multidimensional spheres. (English. Russian original) Zbl 1471.70005

J. Math. Sci., New York 236, No. 6, 687-701 (2019); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 137, 104-117 (2017).
MSC:  70E40 37E10 37N05
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Phase portraits of dynamical equations of motion of a rigid body in a resistive medium. (English. Russian original) Zbl 1423.70015

J. Math. Sci., New York 233, No. 3, 398-425 (2018); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 135 (2017).
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Low-dimensional and multidimensional pendulums in nonconservative fields. II. (English. Russian original) Zbl 1423.70020

J. Math. Sci., New York 233, No. 3, 301-397 (2018); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 135 (2017).
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Low-dimensional and multidimensional pendulums in nonconservative fields. I. (English. Russian original) Zbl 1423.70019

J. Math. Sci., New York 233, No. 2, 173-299 (2018); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 134 (2017).
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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).
MSC:  70E45 70E40 37J05
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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).
MSC:  37J35 70E40 70E45
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Integrable cases in the dynamics of a multi-dimensional rigid body in a nonconservative field in the presence of a tracking force. (English. Russian original) Zbl 1353.70021

J. Math. Sci., New York 214, No. 6, 865-891 (2016); translation from Fundam. Prikl. Mat. 19, No. 3, 187-222 (2014).
MSC:  70E40 37J30
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Simulation of the action of a medium on a conical body and the family of phase portraits in the space of quasivelocities. (English. Russian original) Zbl 1353.70016

J. Appl. Mech. Tech. Phys. 56, No. 4, 612-617 (2015); translation from Prikl. Mekh. Tekh. Fiz. 56, No. 4, 85-91 (2015).
MSC:  70E40
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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).
MSC:  70E45 70E40
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On the construction of the general solution of a class of complex nonautonomous equations. (English. Russian original) Zbl 1354.34029

J. Math. Sci., New York 204, No. 6, 787-799 (2015); translation from Sovrem. Mat. Prilozh. 88 (2013).
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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).
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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).
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Dynamical pendulum-like nonconservative systems. (English) Zbl 1302.70051

Awrejcewicz, Jan (ed.), Applied non-linear dynamical systems. Selected papers based on the presentations at the 12th international conference “Dynamical systems-theory and applications”, DSTA, Łódź, Poland, December 2–5, 2013. Cham: Springer (ISBN 978-3-319-08265-3/hbk; 978-3-319-08266-0/ebook). Springer Proceedings in Mathematics & Statistics 93, 503-525 (2014).
MSC:  70H20 70H33 70E40
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Complete list of first integrals for dynamic equations of motion of a solid body in a resisting medium with consideration of linear damping. (English. Russian original) Zbl 1353.70008

Mosc. Univ. Mech. Bull. 67, No. 4, 92-95 (2012); translation from Vestn. Mosk. Univ., Ser. I 67, No. 4, 44-47 (2012).
MSC:  70E15
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Geometric and dynamical invariants of integrable Hamiltonian and dissipative systems. (English. Russian original) Zbl 1353.37121

J. Math. Sci., New York 180, No. 4, 365-530 (2012); translation from Fundam. Prikl. Mat. 16, No. 4, 3-229 (2010).
MSC:  37J35 37N05 70H06
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Comparison of complete integrability cases in dynamics of a two-, three-, and four-dimensional rigid body in a nonconservative field. (English. Russian original) Zbl 1277.37104

J. Math. Sci., New York 187, No. 3, 346-359 (2012); translation from Sovrem. Mat. Prilozh. 76, 84-99 (2012).
MSC:  37N05 70E40 37J35
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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).
MSC:  70E40 70E45 37J35
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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
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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).
MSC:  70E40 70E45
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On integrability in elementary functions of certain classes of nonconservative dynamical systems. (English. Russian original) Zbl 1188.37003

J. Math. Sci., New York 161, No. 5, 734-778 (2009); translation from Sovrem. Mat. Prilozh. 62 (2009).
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New cases of full integrability in dynamics of a dynamically symmetric four-dimensional solid in a nonconservative field. (English. Russian original) Zbl 1347.70010

Dokl. Phys. 54, No. 3, 155-159 (2009); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk, 425, No. 3, 338-342 (2009).
MSC:  70E40 37N15
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Integrability in elementary functions of some classes of dynamical systems. (English. Russian original) Zbl 1212.70011

Mosc. Univ. Mech. Bull. 63, No. 3, 53-59 (2008); translation from Vestn. Mosk. Univ., Ser. I 2008, No. 3, 43-49 (2008).
MSC:  70H06 37J35
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New integrable cases in dynamics of a medium-interacting body with allowance for dependence of resistance force moment on angular velocity. (Russian, English) Zbl 1189.70045

Prikl. Mat. Mekh. 72, No. 2, 273-287 (2008); translation in J. Appl. Math. Mech. 72, No. 2, 169-179 (2008).
MSC:  70F99 70E18
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Methods of analysis of various dissipation dynamical systems in dynamics of a rigid body. (Методы анализа динамических систем с переменной диссипацней в динамике твердого тела.) (Russian) Zbl 1334.70001

Moscow: Ekzamen (ISBN 5-472-02476-5). 350 p. (2007).
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First integrals of motion equations of a generalized gyroscope in \(\mathbb R^n\). (Russian, English) Zbl 1127.70003

Vestn. Mosk. Univ., Ser. I 2003, No. 5, 37-41 (2003); translation in Mosc. Univ. Math. Bull. 58, No. 5, 25-29 (2003).
MSC:  70E05 70K99
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Some questions of the qualitative theory of ordinary differential equations and dynamics of a rigid body interacting with a medium. (English) Zbl 1006.34035

J. Math. Sci., New York 110, No. 2, 2528-2557 (2002); translation from Dynamical Systems - 10, Itogi Nauki Tekhn., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 79 (2000).
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Complete integrability of equations of motion of a spatial pendulum placed in an incident medium. (English. Russian original) Zbl 1051.70509

Mosc. Univ. Mech. Bull. 56, No. 5, 1-7 (2001); translation from Vestn. Mosk. Univ., Ser. I 2001, No. 5, 22-28 (2001).
MSC:  70E40 70H06 37N05
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Solving the problem of differential diagnostics by the method of statistical tests. (English. Russian original) Zbl 1074.70572

Mosc. Univ. Mech. Bull. 56, No. 1, 1-3 (2001); translation from Vestn. Mosk. Univ., Ser. I 2001, No. 1, 29-31 (2001).
MSC:  70Q05 93C15 93E03
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The definition of relative robustness and a two-parameter family of phase portraits in the dynamics of a rigid body. (English. Russian original) Zbl 0874.70006

Russ. Math. Surv. 51, No. 1, 165-166 (1996); translation from Usp. Mat. Nauk 51, No. 1, 175-176 (1996).
MSC:  70E15 70G10 37C75
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