Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics]
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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics], 2006, Volume 2, Number 4, Pages 445–452 (Mi nd183)  

This article is cited in 8 scientific papers (total in 8 papers)

Rolling of a heterotgeneous ball over a sphere without sliding and spinning

A. V. Borisovab, I. S. Mamaevab

a Udmurt State University
b Institute of Computer Science
Full-text PDF (162 kB) Citations (8)
Abstract: Consider the problem of rolling a dynamically asymmetric balanced ball (the Chaplygin ball) over a sphere. Suppose that the contact point has zero velocity and the projection of the angular velocity to the normal vector of the sphere equals zero. This model of rolling differs from the classical one. It can be realized, in some approximation, if the ball is rubber coated and the sphere is absolutely rough. Recently, Koiller and Ehlers pointed out the measure and the Hamiltonian structure for this problem. Using this structure we construct an isomorphism between this problem and the problem of the motion of a point on a sphere in some potential field. The integrable cases are found.
Keywords: Chaplygin ball, rolling model, Hamiltonian structure.
Document Type: Article
UDC: 532.5
MSC: 37N15
Language: Russian
Citation: A. V. Borisov, I. S. Mamaev, “Rolling of a heterotgeneous ball over a sphere without sliding and spinning”, Nelin. Dinam., 2:4 (2006), 445–452
Citation in format AMSBIB
\Bibitem{BorMam06}
\by A.~V.~Borisov, I.~S.~Mamaev
\paper Rolling of a heterotgeneous ball over a sphere without sliding and spinning
\jour Nelin. Dinam.
\yr 2006
\vol 2
\issue 4
\pages 445--452
\mathnet{http://mi.mathnet.ru/nd183}
Linking options:
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  • https://www.mathnet.ru/eng/nd/v2/i4/p445
  • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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