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It doesn't take much to
argue that a totally elastic collision is one in which the two
objects bounce off with the same velocity as they came in with.
Not only does this
avoid the consideration of energy, but it also allows a very
straightforward approach to real collisions--ones where the final
velocities in the C0fM frame are less than the initial velocities. It
is not difficult to show that the fractional change in outgoing
velocity over the incoming one must be the same for both objects, and
this fractional change is just the coefficient of restitution.