A mathematical billiard consists of a domain, say, in
billiard table), and a point-mass (a billiard ball) tha
the domain freely. This means that the point moves a
line with a constant speed until it hits the boundary.
off the boundary is elastic and subject to a familiar
of incidence equals the angle of reflection. After the
point continues its free motion with the new velocity u
boundary again, etc.; see figure 1.1.
Figure 1.1. Billiard reflection
An equivalent description of the billiard reflection
impact point, the velocity of the incoming billiard ball