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Two hard balls hang on separate strings. They can collide in continuation if you move rhythmically your hand. Each of the balls will move along its own semicircle and collide with the other one in the highest and lowest position. If we do not supply constantly the motion to the balls, they will stop collisions immediately. There are no ideal elastic collisions and in each collision the balls loose some energy, at least for making noise.

The balls have the same mass and they collide centrally with the same velocity, but the directions of the velocities are opposite. As a result, they bounce off each other in opposite directions, again with the same velocities. If one of them stops, then, after next collision, they bounce off each other at a right angle (or one of them stops, like in the Newton's Pendulum).

But generally speaking , this problem is rather complicated.