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Nelin. Dinam., 2013, Volume 9, Number 2, Pages 257–265 (Mi nd389)  

This article is cited in 2 scientific papers (total in 2 papers)

Integrability and stochastic behavior in some nonholonomic dynamics problems

Ivan A. Bizyaeva, Alexey O. Kazakovb

a Institute of Computer Science; Laboratory of nonlinear analysis and the design of new types of vehicles, Udmurt State University, Izhevsk, Russia
b Research Institute for Applied Mathematics and Cybernetics, Nizhnii Novgorod, Russia

Abstract: In this paper, we investigate the dynamics of systems describing the rolling without slipping and spinning (rubber rolling) of an ellipsoid on a plane and a sphere. We research these problems using Poincaré maps, which investigation helps to discover a new integrable case.

Keywords: nonholonomic constraint, invariant measure, first integral, Poincaré map, integrability and chaos.

Full text: PDF file (517 kB)
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Document Type: Article
UDC: 531.38
MSC: 37J60, 37J35
Received: 03.04.2013
Revised: 21.05.2013

Citation: Ivan A. Bizyaev, Alexey O. Kazakov, “Integrability and stochastic behavior in some nonholonomic dynamics problems”, Nelin. Dinam., 9:2 (2013), 257–265

Citation in format AMSBIB
\Bibitem{BizKaz13}
\by Ivan~A.~Bizyaev, Alexey~O.~Kazakov
\paper Integrability and stochastic behavior in some nonholonomic dynamics problems
\jour Nelin. Dinam.
\yr 2013
\vol 9
\issue 2
\pages 257--265
\mathnet{http://mi.mathnet.ru/nd389}


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    This publication is cited in the following articles:
    1. A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Ierarkhiya dinamiki pri kachenii tverdogo tela bez proskalzyvaniya i vercheniya po ploskosti i sfere”, Nelineinaya dinam., 9:2 (2013), 141–202  mathnet
    2. A. O. Kazakov, “Fenomeny khaoticheskoi dinamiki v zadache o kachenii rok-n-rollera bez vercheniya”, Nelineinaya dinam., 9:2 (2013), 309–325  mathnet
  • Нелинейная динамика
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