 | | 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: | | 10512 |
| In Russian (ΟΜΜ): | | 9713
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| In English (J. Appl. Math. Mech.): | | 799 |
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| << Previous article | Volume 80, Issue 4 / 2016 | Next article >> |
| A.P. Markeev, "The stability of two-link trajectories of a Birkhoff billiard," J. Appl. Math. Mech. 80 (4), 280-289 (2016) |
| Year |
2016 |
Volume |
80 |
Issue |
4 |
Pages |
280-289 |
| DOI |
10.1016/j.jappmathmech.2016.09.002 |
| Title |
The stability of two-link trajectories of a Birkhoff billiard |
| Author(s) |
A.P. Markeev (Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow, Russia, markeev@ipmnet.ru) |
| Abstract |
The inertial motion of a particle in a plane region bounded by two analytical curves is studied. Within the region the particle moves in a straight line and the collisions with the boundary curves are considered to be absolutely elastic. It is assumed that the boundary curves allow the existence of a two-link periodic trajectory. The nonlinear problem of stability of this trajectory is analysed. An algorithm for constructing the area-preserving mapping corresponding to this problem in the form of series is explained. General conditions are obtained for the stability and instability of a two-link trajectory, expressed in terms of the coefficients of the series specifying the boundary curves. Some specific examples are considered. |
| Received |
29 December 2015 |
| Link to Fulltext |
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