Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics]
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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics], 2010, Volume 6, Number 4, Pages 869–889 (Mi nd10)  

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

Rolling of a homogeneous ball over a dynamically asymmetric sphere

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

Institute of Computer Science
Full-text PDF (486 kB) Citations (3)
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Abstract: We consider a novel mechanical system consisting of two spherical bodies rolling over each other, which is a natural extension of the famous Chaplygin problem of rolling motion of a ball on a plane. In contrast to the previously explored non-holonomic systems, this one has a higher dimension and is considerably more complicated. One remarkable property of our system is the existence of “clandestine” linear in momenta first integrals. For a more trivial integrable system, their counterparts were discovered by Chaplygin. We have also found a few cases of integrability.
Keywords: nonholonomic constraint, rolling motion, Chaplygin ball, integral, invariant measure.
Received: 04.11.2010
Document Type: Article
UDC: 532.5
MSC: 37N15
Language: Russian
Citation: A. V. Borisov, A. A. Kilin, I. S. Mamaev, “Rolling of a homogeneous ball over a dynamically asymmetric sphere”, Nelin. Dinam., 6:4 (2010), 869–889
Citation in format AMSBIB
\Bibitem{BorKilMam10}
\by A.~V.~Borisov, A.~A.~Kilin, I.~S.~Mamaev
\paper Rolling of a homogeneous ball over a dynamically asymmetric sphere
\jour Nelin. Dinam.
\yr 2010
\vol 6
\issue 4
\pages 869--889
\mathnet{http://mi.mathnet.ru/nd10}
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  • https://www.mathnet.ru/eng/nd/v6/i4/p869
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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