0
2013
Impact Factor

# I. Gorelyshev

ul. Profsoyuznaya 84/32, 117997, Moscow, Russian Federation
Space Research Institute, Russian Academy of Sciences

## Publications:

 Gorelyshev I. V. On the full number of collisions in certain one-dimensional billiard problems 2006, vol. 11, no. 1, pp.  61-66 Abstract In the present work we consider motion of a light particle between a wall and a massive particle. Collisions in the system are elastic. In [1] the full number of collisions in this system was calculated. It turned out to be approximately equal to the product of number $\pi$ and the square root of ratio of the particles' masses. This formula was derived using reduction of the system to a billiard. In the present work this result is derived by means of the adiabatic perturbation theory for systems with impacts [2]. Keywords: canonical perturbation theory, adiabatic approximation, billiards, impacts Citation: Gorelyshev I. V.,  On the full number of collisions in certain one-dimensional billiard problems , Regular and Chaotic Dynamics, 2006, vol. 11, no. 1, pp. 61-66 DOI: 10.1070/RD2006v011n01ABEH000334