Аннотация:
This paper can be regarded as a continuation of our previous work [1, 2] on the hierarchy of the dynamical behavior of nonholonomic systems. We consider different mechanical systems with nonholonomic constraints; in particular, we examine the existence of tensor invariants (laws of conservation) and their connection with the behavior of a system. Considerable attention is given to the possibility of conformally Hamiltonian representation of the equations of motion, which is mainly used for the integration of the considered systems.
Ключевые слова:
nonholonomic systems, implementation of constraints, conservation laws, hierarchy of dynamics, explicit integration.
Поступила в редакцию: 04.04.2008 Принята в печать: 30.08.2008
Образец цитирования:
A. V. Borisov, I. S. Mamaev, “Conservation Laws, Hierarchy of Dynamics and Explicit Integration of Nonholonomic Systems”, Regul. Chaotic Dyn., 13:5 (2008), 443–490
\RBibitem{BorMam08}
\by A.~V.~Borisov, I.~S.~Mamaev
\paper Conservation Laws, Hierarchy of Dynamics and Explicit Integration of Nonholonomic Systems
\jour Regul. Chaotic Dyn.
\yr 2008
\vol 13
\issue 5
\pages 443--490
\mathnet{http://mi.mathnet.ru/rcd595}
\crossref{https://doi.org/10.1134/S1560354708050079}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2448343}
\zmath{https://zbmath.org/?q=an:1229.70038}
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https://www.mathnet.ru/rus/rcd595
https://www.mathnet.ru/rus/rcd/v13/i5/p443
Эта публикация цитируется в следующих 107 статьяx:
Federico Talamucci, “Nonlinear nonholonomic systems: a simple approach and various examples”, Meccanica, 59:3 (2024), 333
Alexander A. Kilin, Elena N. Pivovarova, “Bifurcation analysis of the problem of a “rubber” ellipsoid of revolution rolling on a plane”, Nonlinear Dyn, 2024
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)
Theresa E. Honein, Oliver M. O'Reilly, “On the dynamics of transporting rolling cylinders”, Nonlinear Dyn, 2024
Alexander A. Kilin, Elena N. Pivovarova, “Dynamics of an Unbalanced Disk
with a Single Nonholonomic Constraint”, Regul. Chaotic Dyn., 28:1 (2023), 78–106
A. A. Kilin, T. B. Ivanova, “The Integrable Problem of the Rolling Motion
of a Dynamically Symmetric Spherical Top
with One Nonholonomic Constraint”, Rus. J. Nonlin. Dyn., 19:1 (2023), 3–17
A. A. Kilin, T. B. Ivanova, “The Problem of the Rolling Motion
of a Dynamically Symmetric Spherical Top
with One Nonholonomic Constraint”, Rus. J. Nonlin. Dyn., 19:4 (2023), 533–543
Vladimir Dragović, Borislav Gajić, Božidar Jovanović, “Gyroscopic Chaplygin Systems and Integrable Magnetic Flows on Spheres”, J Nonlinear Sci, 33:3 (2023)
Jaume Llibre, Rafael Ramírez, Valentín Ramírez, Dynamics through First-Order Differential Equations in the Configuration Space, 2023, 33
David Perrella, Nathan Duignan, David Pfefferlé, “Existence of global symmetries of divergence-free fields with first integrals”, Journal of Mathematical Physics, 64:5 (2023)
Evgeniya A. Mikishanina, “Dynamics of the Chaplygin sphere with additional constraint”, Commun. Nonlinear Sci. Numer. Simul., 117 (2023), 106920–15
Ivan A. Bizyaev, Ivan S. Mamaev, “Permanent Rotations in Nonholonomic Mechanics.
Omnirotational Ellipsoid”, Regul. Chaotic Dyn., 27:6 (2022), 587–612
Е. М. Артемова, А. А. Килин, Ю. В. Коробейникова, “Исследование орбитальной устойчивости прямолинейных качений роллер-рейсера по вибрирующей плоскости”, Вестн. Удмуртск. ун-та. Матем. Мех. Компьют. науки, 32:4 (2022), 615–629
Alexander A. Kilin, Elena N. Pivovarova, “A Particular Integrable Case in the Nonautonomous Problem
of a Chaplygin Sphere Rolling on a Vibrating Plane”, Regul. Chaotic Dyn., 26:6 (2021), 775–786
Garcia-Naranjo L. U. I. S. C., Vermeeren M. A. T. S., “Structure Preserving Discretization of Time-Reparametrized Hamiltonian Systems With Application to Nonholonomic Mechanics”, J. Comput. Dynam., 8:3 (2021), 241–271
Alexander Kilin, Elena Pivovarova, 2021 International Conference “Nonlinearity, Information and Robotics” (NIR), 2021, 1
Alexey V. Borisov, Evgeniya A. Mikishanina, “Two Nonholonomic Chaotic Systems. Part II. On the Rolling of a Nonholonomic Bundle of Two Bodies”, Regul. Chaotic Dyn., 25:4 (2020), 392–400
Elizaveta M. Artemova, Yury L. Karavaev, Ivan S. Mamaev, Evgeny V. Vetchanin, “Dynamics of a Spherical Robot with Variable Moments of Inertia and a Displaced Center of Mass”, Regul. Chaotic Dyn., 25:6 (2020), 689–706
А. А. Килин, Е. Н. Пивоварова, “Неинтегрируемость задачи о качении сферического волчка по вибрирующей плоскости”, Вестн. Удмуртск. ун-та. Матем. Мех. Компьют. науки, 30:4 (2020), 628–644
Vladimir Dragović, Borislav Gajić, Božidar Jovanović, “Demchenko's nonholonomic case of a gyroscopic ball rolling without sliding over a sphere after his 1923 Belgrade doctoral thesis”, Theor. Appl. Mech., 47:2 (2020), 257–287
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