When a moving ball collides elastically with an identical, initially stationary ball, the incident ball will either come to rest (head-on collision; see Fig. 1) or will acquire a velocity that is perpendicular to that acquired by the target ball (oblique collision; see Fig. 2). These two possible outcomes are related in an interesting way, which we describe in this paper.

We neglect all nonconservative forces, hence the total kinetic energy is conserved.
In reality, the objects are not perfectly rigid, so the “point of contact” between them may actually be an area. The “normal forces” in our discussion are spatial averages.
If we view the collision from a reference frame that is moving with constant velocity v, what we see is a head-on collision in the // direction between m1 (which has initial velocity v//) and m2, which is initially at rest in that direction.
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