 | | 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
(print version) |
Archive of Issues
| Total articles in the database: | | 10522 |
| In Russian (ΟΜΜ): | | 9723
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| In English (J. Appl. Math. Mech.): | | 799 |
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| << Previous article | Volume 73, Issue 2 / 2009 | Next article >> |
| 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 |
| Link to Fulltext |
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