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Regular and Chaotic Dynamics, 2011, Volume 16, Issue 6, Pages 653–662
DOI: https://doi.org/10.1134/S1560354711060062 (Mi rcd461) 		 
This article is cited in 5 scientific papers (total in 5 papers)

On the Model of Non-holonomic Billiard

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

Institute of Computer Science, Udmurt State University, ul. Universitetskaya 1, Izhevsk 426034, Russia
Citations (5)
DOI: https://doi.org/10.1134/S1560354711060062
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.
Received: 06.11.2010
Accepted: 14.07.2011
Document Type: Article
MSC: 34D20, 70E40, 37J35
Language: English
Citation: Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “On the Model of Non-holonomic Billiard”, Regul. Chaotic Dyn., 16:6 (2011), 653–662
Citation in format AMSBIB
\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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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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