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

Russian Academy of Sciences
in January 1936
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IssuesArchive of Issues2016-4pp.280-289

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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,
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
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