Аннотация:
In this paper, we investigate the dynamics of systems describing the rolling without slipping and spinning (rubber rolling) of various rigid bodies on a plane and a sphere. It is shown that a hierarchy of possible types of dynamical behavior arises depending on the body’s surface geometry and mass distribution. New integrable cases and cases of existence of an invariant measure are found. In addition, these systems are used to illustrate that the existence of several nontrivial involutions in reversible dissipative systems leads to quasi-Hamiltonian behavior.
This work was carried out at the Udmurt State University and was supported by Grant of the President of the Russian Federation for Support of Leading Scientific Schools NSh-2519.2012.1 “Dynamical Systems of Classical Mechanics and Control Problems”, Analytic Departmental Target Program “Development of Scientific Potential of Higher Schools” (1.1248.2011), Analytic Depart-mental Target Program ”Development of Scientific Potential of Higher Schools” (1.7734.2013), Federal Target Program “Scientific and Scientific-Pedagogical Personnel of Innovative Russia” (Agreement №14.A37.21.1935).
Поступила в редакцию: 12.03.2013 Принята в печать: 08.05.2013
Образец цитирования:
Alexey V. Borisov, Ivan S. Mamaev, Ivan A. Bizyaev, “The Hierarchy of Dynamics of a Rigid Body Rolling without Slipping and Spinning on a Plane and a Sphere”, Regul. Chaotic Dyn., 18:3 (2013), 277–328
\RBibitem{BorMamBiz13}
\by Alexey V. Borisov, Ivan S. Mamaev, Ivan A. Bizyaev
\paper The Hierarchy of Dynamics of a Rigid Body Rolling without Slipping and Spinning on a Plane and a Sphere
\jour Regul. Chaotic Dyn.
\yr 2013
\vol 18
\issue 3
\pages 277--328
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\crossref{https://doi.org/10.1134/S1560354713030064}
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Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd114
https://www.mathnet.ru/rus/rcd/v18/i3/p277
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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
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Ivan S. Mamaev, Evgeny V. Vetchanin, “Dynamics of Rubber Chaplygin Sphere under Periodic Control”, Regul. Chaotic Dyn., 25:2 (2020), 215–236
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