✦ LIBER ✦

The dynamics of a Chaplygin sleigh

✍ Scribed by A.V. Borisov; I.S. Mamayev

Publisher: Elsevier Science
Year: 2009
Tongue: English
Weight: 285 KB
Volume: 73
Category: Article
ISSN: 0021-8928
DOI: 10.1016/j.jappmathmech.2009.04.005

No coin nor oath required. For personal study only.

✦ Synopsis

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.

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