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Nelin. Dinam., 2010, Volume 6, Number 2, Pages 373–385 (Mi nd47)  

This article is cited in 1 scientific paper (total in 2 paper)

Outstanding problems of dynamics

On the model of non-holonomic billiard

A. V. Borisov, A. A. Kilin, I. S. Mamaev

Institute of Computer Science

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 mapping, nonintegrability, periodic solution, nonholonomic constraint, integral of motion.

Full text: PDF file (237 kB)
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Document Type: Article
UDC: 531.38
MSC: 34D20, 70E40, 37J35
Received: 02.06.2010

Citation: A. V. Borisov, A. A. Kilin, I. S. Mamaev, “On the model of non-holonomic billiard”, Nelin. Dinam., 6:2 (2010), 373–385

Citation in format AMSBIB
\Bibitem{BorKilMam10}
\by A.~V.~Borisov, A.~A.~Kilin, I.~S.~Mamaev
\paper On the model of non-holonomic billiard
\jour Nelin. Dinam.
\yr 2010
\vol 6
\issue 2
\pages 373--385
\mathnet{http://mi.mathnet.ru/nd47}
\elib{http://elibrary.ru/item.asp?id=15002242}


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    This publication is cited in the following articles:
    1. A. V. Borisov, A. A. Kilin, I. S. Mamaev, “Kachenie odnorodnogo shara po dinamicheski nesimmetrichnoi sfere”, Nelineinaya dinam., 6:4 (2010), 869–889  mathnet
    2. “Problemy teorii udara. Billiardy”, Nelineinaya dinam., 6:2 (2010), 371–372  mathnet
  • Нелинейная динамика
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