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Better yet, consider the (not quite physically realizable) case of a
particle attached to a massless vertical stick and another particle
initially moving horizontally that strikes and sticks to the end of
the stick. Is this a totally inelastic collision? Note that, in the
CM frame, the final kinetic energy is equal to the initial kinetic
energy.
Now some (myself included) would claim that rotational kinetic energy
is "internal" energy. Thus, in the CM frame, the collision
completely "internalized" the initial bulk translational kinetic
energy of the two colliding objects and, in that sense, was indeed
totally inelastic. (Note also that the separation speed is zero in
keeping with the coefficient of restitution based definition of
"totally inelastic.")