Suppose two rigid bodies collide head-on in a vacuum. Will the collision be elastic or inelastic?
In most rigid body computer systems you have to specificy a coefficient of restitution for the collision, so the answer would depend on that. But this is a post-hoc mechanism used so we can better model real world systems; it's not a natural consequence of our assumption that bodies are rigid.
For elastic collisions in the real world bodies would deform the relax over some amount of time which provides the mechanism for impulses to change the directions of the bodies. But in a world of only rigid bodies they can't do that.
If collisions are inelastic, I can't see a plausible mechanism that would absorb the excess energy. The bodies can't deform by definition, so it can't be that. We could say the bodies warm up, but temperature is not normally included as a property in rigid body systems and I'm not even sure if it would be a well defined property in such a system without introducing a whole slew of other properties and phyical laws.
Perhaps the rigid body assumption violates conservation of energy? But that doesn't seem right since conservation of energy comes from time symmetry (from Noether's Theorem), which should still hold for a rigid body system.
Perhaps the result of collisions between rigid bodies is ill-defined because the concept of rigid bodies is non-physical? But there are lots of non-physical simplifications used in physics and mathematics that are still self-consistent. Maybe what happens when two bodies collide is another assumption you have to explicitly make for the system to be self-consistent?
Lots of questions but I'm not sure how to approach looking for an answer.