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Nelin. Dinam., 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

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.

Full text: PDF file (486 kB)
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Document Type: Article
UDC: 532.5
MSC: 37N15
Received: 04.11.2010

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. V. Borisov, I. S. Mamaev, “Dinamika shara Chaplygina s polostyu, zapolnennoi zhidkostyu”, Nelineinaya dinam., 8:1 (2012), 103–111  mathnet
    2. A. V. Borisov, I. S. Mamaev, “Topologicheskii analiz odnoi integriruemoi sistemy, svyazannoi s kacheniem shara po sfere”, Nelineinaya dinam., 8:5 (2012), 957–975  mathnet
    3. Alexey V. Borisov, Ivan S. Mamaev, “The Dynamics of the Chaplygin Ball with a Fluid-filled Cavity”, Regul. Chaotic Dyn., 18:5 (2013), 490–496  mathnet  crossref  mathscinet  zmath
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