Rolling of a homogeneous ball over a dynamically asymmetric sphere

  • Alexey V. Borisov
  • Alexander A. Kilin
  • Ivan S. Mamaev
Article

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 

MSC2010 numbers

37N15 

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Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  • Alexey V. Borisov
    • 1
  • Alexander A. Kilin
    • 1
  • Ivan S. Mamaev
    • 1
  1. 1.Institute of Computer ScienceUdmurt State UniversityIzhevskRussia

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