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Regular and Chaotic Dynamics, 2006, Volume 11, Issue 1, Pages 61–66
DOI: https://doi.org/10.1070/RD2006v011n01ABEH000334 (Mi rcd657) 		 
This article is cited in 2 scientific papers (total in 2 papers)

On the full number of collisions in certain one-dimensional billiard problems

I. V. Gorelyshev

Space Research Institute, RAS, 84/32, Profsoyuznaya str., 117997 Moscow, Russia
Citations (2)
DOI: https://doi.org/10.1070/RD2006v011n01ABEH000334
Abstract: In the present work we consider motion of a light particle between a wall and a massive particle. Collisions in the system are elastic. In [1] the full number of collisions in this system was calculated. It turned out to be approximately equal to the product of number $\pi$ and the square root of ratio of the particles' masses. This formula was derived using reduction of the system to a billiard. In the present work this result is derived by means of the adiabatic perturbation theory for systems with impacts [2].
Keywords: canonical perturbation theory, adiabatic approximation, billiards, impacts.
Received: 15.07.2005
Accepted: 05.12.2005
Bibliographic databases:
Document Type: Article
MSC: 70G60, 70H09, 70H11, 70K70
Language: English
Citation: I. V. Gorelyshev, “On the full number of collisions in certain one-dimensional billiard problems”, Regul. Chaotic Dyn., 11:1 (2006), 61–66
Citation in format AMSBIB
\Bibitem{Gor06}
\by I. V. Gorelyshev
\paper On the full number of collisions in certain one-dimensional billiard problems
\jour Regul. Chaotic Dyn.
\yr 2006
\vol 11
\issue 1
\pages 61--66
\mathnet{http://mi.mathnet.ru/rcd657}
\crossref{https://doi.org/10.1070/RD2006v011n01ABEH000334}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2222432}
\zmath{https://zbmath.org/?q=an:1133.70329}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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