ul. Profsoyuznaya 84/32, 117997, Moscow, Russian Federation
Space Research Institute, Russian Academy of Sciences
Gorelyshev I. V.
On the full number of collisions in certain one-dimensional billiard problems
2006, vol. 11, no. 1, pp. 61-66
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  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 .