Coefficient of restitution for elastic disks

We compute the coefficient of restitution epsilon Starting from a microscop ic model of elastic disks. Collisions are found to be inelastic, in general , with a finite fraction of translational energy being transferred to elast ic vibrations. The coefficient of restitution depends on the relative veloc ity of the colliding disks, such that collisions become increasingly more i nelastic for larger relative velocities. The predictions of the model are i n agreement with the approach of Hertz [J. Reine Angew. Math. 92, 156 (1882 )] in the quasistatic limit. The. coefficient of restitution depends on the elastic constants of the material via Poisson's number. The elastic vibrat ions absorb kinetic energy more effectively for soft materials with low rat ios of shear to bulk modulus.