Regular and Chaotic Dynamics

, Volume 18, Issue 5, pp 490–496 | Cite as

The dynamics of the chaplygin ball with a fluid-filled cavity

  • Alexey V. Borisov
  • Ivan S. Mamaev


We consider the problem of rolling of a ball with an ellipsoidal cavity filled with an ideal fluid, which executes a uniform vortex motion, on an absolutely rough plane. We point out the case of existence of an invariant measure and show that there is a particular case of integrability under conditions of axial symmetry.


vortex motion nonholonomic constraint Chaplygin ball invariant measure integrability rigid body ideal fluid 

MSC2010 numbers

70E18 76B47 


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Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.Institute of Computer Science; Laboratory of Nonlinear Analysis and the Design of New Types of VehiclesUdmurt State UniversityIzhevskRussia
  2. 2.A.A. Blagonravov Mechanical Engineering Research Institute of RASMoscowRussia
  3. 3.Institute of Mathematics and Mechanics of the Ural Branch of RASYekaterinburgRussia

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