The work of A V Borisov was carried out within the framework of the basic part of the State assignment for institutes of higher education. The work of I S Mamaev was supported by the grant no 14-50-00005 of the Russian Science Foundation.
Поступила в редакцию: 21.05.2014 Принята в печать: 07.05.2015
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Тип публикации:
Статья
Язык публикации: английский
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https://www.mathnet.ru/rus/nonli1
Эта публикация цитируется в следующих 26 статьяx:
José F. Cariñena, Partha Guha, “Lichnerowicz-Witten differential, symmetries and locally conformal symplectic structures”, Journal of Geometry and Physics, 210 (2025), 105418
Luis C. García-Naranjo, Juan C. Marrero, David Martín de Diego, Paolo E. Petit Valdés, “Almost-Poisson Brackets for Nonholonomic Systems with Gyroscopic Terms and Hamiltonisation”, J Nonlinear Sci, 34:6 (2024)
Vladimir Dragović, Borislav Gajić, Božidar Jovanović, “Gyroscopic Chaplygin Systems and Integrable Magnetic Flows on Spheres”, J Nonlinear Sci, 33:3 (2023)
J F Cariñena, Eduardo Martínez, Miguel C Muñoz-Lecanda, “Sundman transformation and alternative tangent structures”, J. Phys. A: Math. Theor., 56:18 (2023), 185202
Luis C García-Naranjo, Juan C Marrero, “The geometry of nonholonomic Chaplygin systems revisited”, Nonlinearity, 33:3 (2020), 1297
Andrey V. Tsiganov, “Hamiltonization and Separation of Variables for a Chaplygin Ball on a Rotating Plane”, Regul. Chaotic Dyn., 24:2 (2019), 171–186
Borislav Gajić, Božidar Jovanović, “Nonholonomic connections, time reparametrizations, and integrability of the rolling ball over a sphere”, Nonlinearity, 32:5 (2019), 1675
Alexey V. Borisov, Andrey V. Tsiganov, “On the Chaplygin Sphere in a Magnetic Field”, Regul. Chaotic Dyn., 24:6 (2019), 739–754
Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “Different Models of Rolling for a Robot Ball on a Plane as a Generalization of the Chaplygin Ball Problem”, Regul. Chaotic Dyn., 24:5 (2019), 560–582
Luis C García-Naranjo, “Generalisation of Chaplygin's reducing multiplier theorem with an application to multi-dimensional nonholonomic dynamics”, J. Phys. A: Math. Theor., 52:20 (2019), 205203
Alexey Bolsinov, Vladimir S. Matveev, Eva Miranda, Serge Tabachnikov, “Open problems, questions and challenges in finite- dimensional integrable systems”, Phil. Trans. R. Soc. A., 376:2131 (2018), 20170430
I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Dynamics of the Chaplygin ball on a rotating plane”, Russ. J. Math. Phys., 25:4 (2018), 423
А. В. Борисов, И. С. Мамаев, И. А. Бизяев, “Динамические системы с неинтегрируемыми связями: вакономная механика, субриманова геометрия и неголономная механика”, УМН, 72:5 (2017), 3–62; A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanics”, Russian Math. Surveys, 72:5 (2017), 783–840
А. В. Борисов, А. А. Килин, И. С. Мамаев, “Принцип Гамильтона и качение симметричного шара”, Докл. РАН, 474:5 (2017), 558–562; A. V. Borisov, A. A. Kilin, I. S. Mamaev, “The Hamilton principle and the rolling motion of a symmetric ball”, Dokl. Math., 62:6 (2017), 314–317
Isaac A García, Benito Hernández-Bermejo, “Inverse Jacobi multiplier as a link between conservative systems and Poisson structures”, J. Phys. A: Math. Theor., 50:32 (2017), 325204
А.В. БОРИСОВ, А.А. Килин, И. С. Мамаев, “ПРИНЦИП ГАМИЛЬТОНА И КАЧЕНИЕ СИММЕТРИЧНОГО ШАРА, “Доклады Академии наук””, Доклады Академии Наук, 2017, № 5, 558
Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “The Hojman Construction and Hamiltonization of Nonholonomic Systems”, SIGMA, 12 (2016), 012, 19 pp., arXiv: 1510.00181
Alexey V. Borisov, Ivan S. Mamaev, “Adiabatic Invariants, Diffusion and Acceleration in Rigid Body Dynamics”, Regul. Chaotic Dyn., 21:2 (2016), 232–248
Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “Dynamics of the Chaplygin Sleigh on a Cylinder”, Regul. Chaotic Dyn., 21:1 (2016), 136–146
A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “The Jacobi integral in nonholonomic mechanics”, Regul. Chaotic Dyn., 20:3 (2015), 383–400