  We analyze the impact of two equal billiard balls in three ideal situations:
when the balls freely slide on the plane of the billiard, when they roll
without sliding and when one of them freely slides and the other rolls. In all
the cases we suppose that the contact between the balls is smooth. We base our
analysis on some recent general theoretical results on ideal impacts obtained
by means of Differential Geometric Impulsive Mechanics. We use symbolic
computation software to solve the computational difficulties arising by the
high number of degrees of freedom of the system. Some particular but
significative impacts, with opportunely assigned left velocities and positions
of the balls, are analyzed in details. The results admit easy interpretations
that turn out to be in good agreement with the reasonable forecasts and the
behaviours of real systems.
