Abstract:
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.
\Bibitem{BorKilMam11}
\by Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev
\paper On the Model of Non-holonomic Billiard
\jour Regul. Chaotic Dyn.
\yr 2011
\vol 16
\issue 6
\pages 653--662
\mathnet{http://mi.mathnet.ru/rcd461}
\crossref{https://doi.org/10.1134/S1560354711060062}
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https://www.mathnet.ru/eng/rcd/v16/i6/p653
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