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Regular and Chaotic Dynamics, 2008, Volume 13, Issue 3, Pages 221–233
DOI: https://doi.org/10.1134/S1560354708030076
(Mi rcd572)
 

This article is cited in 3 scientific papers (total in 3 papers)

Chaos in a Restricted Problem of Rotation of a Rigid Body with a Fixed Point

A. V. Borisov, A. A. Kilin, I. S. Mamaev

Institute of Computer Science, Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia
Citations (3)
Abstract: In this paper, we consider the transition to chaos in the phase portrait of a restricted problem of rotation of a rigid body with a fixed point. Two interrelated mechanisms responsible for chaotization are indicated: (1) the growth of the homoclinic structure and (2) the development of cascades of period doubling bifurcations. On the zero level of the area integral, an adiabatic behavior of the system (as the energy tends to zero) is noted. Meander tori induced by the break of the torsion property of the mapping are found.
Keywords: motion of a rigid body, phase portrait, mechanism of chaotization, bifurcations.
Received: 13.04.2007
Accepted: 28.10.2007
Bibliographic databases:
Document Type: Article
MSC: 70E17, 65P30, 83C10
Language: English
Citation: A. V. Borisov, A. A. Kilin, I. S. Mamaev, “Chaos in a Restricted Problem of Rotation of a Rigid Body with a Fixed Point”, Regul. Chaotic Dyn., 13:3 (2008), 221–233
Citation in format AMSBIB
\Bibitem{BorKilMam08}
\by A.~V.~Borisov, A.~A.~Kilin, I.~S.~Mamaev
\paper Chaos in a Restricted Problem of Rotation of a Rigid Body with a Fixed Point
\jour Regul. Chaotic Dyn.
\yr 2008
\vol 13
\issue 3
\pages 221--233
\mathnet{http://mi.mathnet.ru/rcd572}
\crossref{https://doi.org/10.1134/S1560354708030076}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2415375}
\zmath{https://zbmath.org/?q=an:1229.70011}
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  • https://www.mathnet.ru/eng/rcd/v13/i3/p221
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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