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Nelin. Dinam., 2010, Volume 6, Number 2, Pages 345–358 (Mi nd43)  

This article is cited in 2 scientific papers (total in 3 papers)

Rubber ball on a plane: singular solutions

A. Yu. Moskvin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The paper deals with the rolling motion of a balanced, dynamically asymmetric ball on a plane without sliding and spinning. The problem is natural but was not considered by classicists. Generalizations of the problem are analyzed for the case where gyrostat and force Brun field are added. To investigate the dynamic behavior of the system some peculiar periodic solutions are described and their stability is examined. By integral mapping, bifurcation diagrams and bifurcation complexes are constructed.

Keywords: bifurcation complex, rubber ball, stability, nonholonomic system.

Full text: PDF file (746 kB)
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Document Type: Article
UDC: 531.133.1
MSC: 37N15
Received: 11.03.2010

Citation: A. Yu. Moskvin, “Rubber ball on a plane: singular solutions”, Nelin. Dinam., 6:2 (2010), 345–358

Citation in format AMSBIB
\Bibitem{Mos10}
\by A.~Yu.~Moskvin
\paper Rubber ball on a plane: singular solutions
\jour Nelin. Dinam.
\yr 2010
\vol 6
\issue 2
\pages 345--358
\mathnet{http://mi.mathnet.ru/nd43}


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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, “Otvet na zamechaniya A. T. Fomenko”, Nelineinaya dinam., 6:4 (2010), 893–895  mathnet
    2. Rozenblat G.M., “the Choice of Physically Realizable Parameters When Studying the Dynamics of Spherical and Ellipsoidal Rigid Bodies”, Dokl. Phys., 60:9 (2015), 412–418  crossref  isi  elib  scopus
    3. Rozenblat G.M., “On the Choice of Physically Realizable Parameters When Studying the Dynamics of Spherical and Ellipsoidal Rigid Bodies”, Mech. Sol., 51:4 (2016), 415–423  crossref  isi
  • Нелинейная динамика
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