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Regular and Chaotic Dynamics, 2008, Volume 13, Issue 4, Pages 239–249
DOI: https://doi.org/10.1134/S1560354708040011 (Mi rcd574) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Nonholonomic mechanics

Stability of Steady Rotations in the Nonholonomic Routh Problem

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

Institute of Computer Science, Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia
Citations (8)
DOI: https://doi.org/10.1134/S1560354708040011
Abstract: We have discovered a new first integral in the problem of motion of a dynamically symmetric ball, subject to gravity, on the surface of a paraboloid. Using this integral, we have obtained conditions for stability (in the Lyapunov sense) of steady rotations of the ball at the upmost, downmost and saddle point.
Keywords: nonholonomic constraint, stationary rotations, stability.
Received: 04.10.2007
Accepted: 16.01.2008
Bibliographic databases:
Document Type: Personalia
MSC: 34D20, 70E40, 37J35
Language: English
Citation: A. V. Borisov, A. A. Kilin, I. S. Mamaev, “Stability of Steady Rotations in the Nonholonomic Routh Problem”, Regul. Chaotic Dyn., 13:4 (2008), 239–249
Citation in format AMSBIB
\Bibitem{BorKilMam08}
\by A.~V.~Borisov, A.~A.~Kilin, I.~S.~Mamaev
\paper Stability of Steady Rotations in the Nonholonomic Routh Problem
\jour Regul. Chaotic Dyn.
\yr 2008
\vol 13
\issue 4
\pages 239--249
\mathnet{http://mi.mathnet.ru/rcd574}
\crossref{https://doi.org/10.1134/S1560354708040011}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2456920}
\zmath{https://zbmath.org/?q=an:1229.70021}
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  • https://www.mathnet.ru/eng/rcd/v13/i4/p239
    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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