  Paradoxes in the impact dynamics of rigid bodies are known to arise in the
presence of friction. We show here that, on specificc 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 which are well separated can come
into contact, and then interpenetrate each other. This paradox can be
constructed 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
O(t^3). The conclusion is that rigid body dynamics is not compatible with the
conservation laws of classical mechanics.
