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Regular and Chaotic Dynamics

, Volume 18, Issue 1–2, pp 159–165 | Cite as

On the motion of a mechanical system inside a rolling ball

  • S. V. BolotinEmail author
  • T. V. Popova
Article

Abstract

We consider a mechanical system inside a rolling ball and show that if the constraints have spherical symmetry, the equations of motion have Lagrangian form. Without symmetry, this is not true.

Keywords

nonholonomic constraint rolling ball Lagrange equations Hamilton principle 

MSC2010 numbers

37J60 70H03 70E18 

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References

  1. 1.
    Arnold, V. I., Kozlov, V.V., and Neishtadt, A. I., Mathematical Aspects of Classical and Celestial Mechanics, Encyclopaedia Math. Sci., vol. 3, Berlin: Springer, 1993, pp. 1–291.CrossRefGoogle Scholar
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    Borisov, A. V. and Mamaev, I. S., Two Non-holonomic Integrable Problems Tracing Back to Chaplygin, Regul. Chaotic Dyn., 2012, vol. 17, no. 2, pp. 191–198.MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Chaplygin, S.A., On Some Generalization of the Area Theorem with Applications to the Problem of Rolling Balls, Matematicheskii Sbornik, 1897, Vol. 20. English translation: Regul. Chaotic Dyn., 2012, vol. 17, no. 2, pp. 199–217.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.University of Wisconsin-MadisonMadisonUSA
  2. 2.V. A. Steklov Mathematical Institute of Russian Academy of SciencesMoscowRussia
  3. 3.M. V. Lomonosov Moscow State UniversityMoscowRussia

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