I understand how the coefficient is applied for purely translating bodies, but once rotation is added, I'm unsure how the law of restitution is applied.
For exactly which points on a pair of bodies is Newton's impact law valid when the bodies are rotating? Different points on a rotating body have different (linear) velocities; I had assumed the impact law was valid only when considering the relative velocity of each body's center of mass, but this seems to not be the case.
I have seen many helpful answers on this site - and some papers - that simply apply the impact law to the relative approach/separation velocities of the impact point on both bodies (computing the linear velocity of the point on each body as $\vec{v}_p = \vec{v}_{COM} + \vec{r}_p \times \vec{\omega}$, which makes perfect sense) but I have never seen a source that suggests that the impact law is valid when applied to relative velocities of arbitrary points on a pair of bodies.
How can this be justified? Is there a derivation for applying the law in this manner?
If this is just how the law is defined, I would love even a reference to a textbook that states this explicitly - wikipedia only brings up the toy examples of either 1D collisions or 2D collisions sans rotation.
