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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 rollwithout sliding and when one of them freely slides and the other rolls. In allthe cases we suppose that the contact between the balls is smooth. We base ouranalysis on some recent general theoretical results on ideal impacts obtainedby means of Differential Geometric Impulsive Mechanics. We use symboliccomputation software to solve the computational difficulties arising by thehigh number of degrees of freedom of the system. Some particular butsignificative impacts, with opportunely assigned left velocities and positionsof the balls, are analyzed in details. The results admit easy interpretationsthat turn out to be in good agreement with the reasonable forecasts and thebehaviours of real systems.

Some results on ideal impacts of billiard balls