Energetic coefficient of restitution for planar impact in multi-rigid-body systems with friction

For two-body collisions, it has been recognized that the coefficient of restitution is not a material property but is affected by initial relative velocity at the contact point as well as orientation of the colliding bodies. This paper obtains expressions for the energetic coefficient of restitution in terms of initial conditions based on the methods of analytical mechanics for impacts of multi-rigid-body systems. We provide two examples. The first example is for two-body collision with friction to validate the rationality of the expressions given by this paper. The example used by Stronge (Mech. Struct. Mach. 29(2) (2001) 239) is served as the second example for comparison with Stronge (2001).