On the Model of Non-holonomic Billiard

    2011, Volume 16, Number 6, pp.  653-662

    Author(s): Borisov A. V., Kilin A. A., Mamaev I. S.

    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.
    Keywords: billiard, impact, point map, nonintegrability, periodic solution, nonholonomic constraint, integral of motion
    Citation: Borisov A. V., Kilin A. A., Mamaev I. S., On the Model of Non-holonomic Billiard, Regular and Chaotic Dynamics, 2011, Volume 16, Number 6, pp. 653-662

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