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).
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