Regular and Chaotic Dynamics

, Volume 17, Issue 2, pp 191–198 | Cite as

Two non-holonomic integrable problems tracing back to Chaplygin

  • Alexey V. Borisov
  • Ivan S. Mamaev


The paper considers two new integrable systems which go back to Chaplygin. The systems consist of a spherical shell that rolls on a plane; within the shell there is a ball or Lagrange’s gyroscope. All necessary first integrals and an invariant measure are found. The solutions are shown to be expressed in terms of quadratures.


non-holonomic constraint integrability invariant measure gyroscope quadrature coupled rigid bodies 

MSC2010 numbers

76M23 34A05 


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Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  1. 1.Institute of Computer ScienceUdmurt State UniversityIzhevskRussia

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