Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics]
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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics], 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
Full-text PDF (237 kB) Citations (2)
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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.
Received: 02.06.2010
Bibliographic databases:
Document Type: Article
UDC: 531.38
MSC: 34D20, 70E40, 37J35
Language: Russian
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{https://elibrary.ru/item.asp?id=15002242}
Linking options:
  • https://www.mathnet.ru/eng/nd47
  • https://www.mathnet.ru/eng/nd/v6/i2/p373
    • This publication is cited in the following 2 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Нелинейная динамика
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    References:90
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