Regular and Chaotic Dynamics

, Volume 16, Issue 6, pp 653–662 | Cite as

On the model of non-holonomic billiard

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


In this paper we develop a new model of non-holonomic billiard that accounts for the intrinsic rotation of the billiard ball. This model is a limit case of the problem of rolling without slipping of a ball without slipping over a quadric surface. The billiards between two parallel walls and inside a circle are studied in detail. Using the three-dimensional-point-map technique, the non-integrability of the non-holonomic billiard within an ellipse is shown.


billiard impact point map nonintegrability periodic solution nonholonomic constraint integral of motion 

MSC2010 numbers

34D20 70E40 37J35 


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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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