Journal of Applied Mathematics and Mechanics (about journal) Journal of Applied
Mathematics and Mechanics

Russian Academy of Sciences
 Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
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IssuesArchive of Issues2009-2pp.156-161

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A.V. Borisov and I.S. Mamayev, "The dynamics of a Chaplygin sleigh," J. Appl. Math. Mech. 73 (2), 156-161 (2009)
Year 2009 Volume 73 Issue 2 Pages 156-161
Title The dynamics of a Chaplygin sleigh
Author(s) A.V. Borisov (Izhevsk, Russia, borisov@ics.rg.ru)
I.S. Mamayev (Izhevsk, Russia, mamaev@ics.org.ru)
Abstract The problem of the motion of a Chaplygin sleigh on horizontal and inclined surfaces is considered. The possibility of representing the equations of motion in Hamiltonian form and of integration using Liouville's theorem (with a redundant algebra of integrals) is investigated. The asymptotics for the rectilinear uniformly accelerated sliding of a sleigh along the line of steepest descent are determined in the case of an inclined plane. The zones in the plane of the initial conditions, corresponding to a different behaviour of the sleigh, are constructed using numerical calculations. The boundaries of these domains are of a complex fractal nature, which enables a conclusion to be drawn concerning the probable character from of the dynamic behaviour.
Received 22 September 2008
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