gent to the boundary line of the configuration spac

#2/Vm2-

Hence the tangential component of the veloc

not change, and the configuration trajectory reflects

cording to the billiard law.

Likewise one considers a collision of the left poin

x = 0; such a collision corresponds to the billiard re

vertical boundary component of the configuration spac

that the system of two elastic point-masses rai and 777,2

is isomorphic to the billiard in the angle arctan \Jm\l

As an immediate corollary, we can estimate the n

sions in our system. Consider the billiard system insi

Instead of reflecting the billiard trajectory in the side

reflect the wedge in the respective side and unfold t

jectory to a straight line; see figure 1.3. This unfold

by geometrical optics, is a very useful trick when stu

inside polygons.

Figur e 1.3. Unfolding a billiard trajectory in a w

Unfolding a billiard trajectory inside a wedge, w

number of reflections is bounded above by |"7r/a] (w

ceiling function, the smallest integer not less than x).