gent to the boundary line of the configuration spac
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).
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