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Nelin. Dinam., 2013, Volume 9, Number 2, Pages 309–325 (Mi nd392)  

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

Chaotic dynamics phenomena in the rubber rock-n-roller on a plane problem

Alexey O. Kazakov

Institute of Computer Science, Izhevsk, Russia

Abstract: In this paper we study a problem of rolling of the dynamically asymmetric ball with displacement center of gravity on a plane without slipping and vertical rotating. It is shown that the dynamics of the ball is significantly affected by the type of reversibility. Depending on the type of the reversibility we found two different types of dynamical chaos: strange attractors and mixed chaotic dynamics. In this paper we describe a strange attractor development, and then its basic properties. A set of criteria by which in numerical experiments mixed dynamics may be distinguished from other types of dynamical chaos are given.

Keywords: rock-n-roller, rubber rolling, reversibility, bifurcation, focus, saddle, separatrix, homoclinic tangency, Lyapunov's exponents, mixed dynamics, strange attractor.

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UDC: 531.38
MSC: 37J60, 37J3
Received: 22.04.2013
Revised: 30.05.2013

Citation: Alexey O. Kazakov, “Chaotic dynamics phenomena in the rubber rock-n-roller on a plane problem”, Nelin. Dinam., 9:2 (2013), 309–325

Citation in format AMSBIB
\Bibitem{Kaz13}
\by Alexey~O.~Kazakov
\paper Chaotic dynamics phenomena in the rubber rock-n-roller on a plane problem
\jour Nelin. Dinam.
\yr 2013
\vol 9
\issue 2
\pages 309--325
\mathnet{http://mi.mathnet.ru/nd392}


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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. V. Borisov, A. O. Kazakov, I. R. Sataev, “Regulyarnye i khaoticheskie attraktory v negolonomnoi modeli volchka Chaplygina”, Nelineinaya dinam., 10:3 (2014), 361–380  mathnet
  • Нелинейная динамика
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