This article is cited in 3 papers

Original papers

On the stability of the two-link trajectory of the parabolic Birkhoff billiards

A. P. Markeev

A.Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101-1, Moscow, 119526, Russia

Abstract: We study the inertial motion of a material point in a planar domain bounded by two coaxial parabolas. Inside the domain the point moves along a straight line, the collisions with the boundary curves are assumed to be perfectly elastic. There is a two-link periodic trajectory, for which the point alternately collides with the boundary parabolas at their vertices, and in the intervals between collisions it moves along the common axis of the parabolas. We study the nonlinear problem of stability of the two-link trajectory of the point.

Keywords: map, canonical transformations, Hamilton system, stability.

UDC: 531.01, 531.36

MSC: 70H05, 70H15, 70E50

Received: 10.02.2016
Revised: 22.02.2016