On a paradox in the impact dynamics of smooth rigid bodies

Paradoxes in the impact dynamics of rigid bodies are known to arise in the presence of friction. We show here that, on specific occasions, in the absence of friction, the conservation laws of classical mechanics are also incompatible with the collisions of smooth, strictly convex rigid bodies. Under the assumption that the impact impulse is along the normal direction to the surface at the contact point, two convex rigid bodies that are well separated can come into contact, and then interpenetrate each other. This paradox can be demonstrated in both 2D and 3D when the collisions are tangential, in which case no momentum or energy transfer between the two bodies is possible. The postcollisional interpenetration can be realized through the contact points or through neighboring points only. The penetration distance is shown to be (Formula presented.). The conclusion is that rigid-body dynamics is not compatible with the conservation laws of classical mechanics.