  Granular systems present surprisingly complicated dynamics. In particular,
nonlinear interactions and energy dissipation play important roles in these
dynamics. Usually, constant coefficients of restitution are introduced
phenomenologically to account for energy dissipation when grains collide. The
collisions are assumed to be instantaneous and to conserve momentum. Here, we
improve on this phenomenology by introducing the dissipation through a viscous
(velocity dependent) term in the equations of motion for two colliding grains.
Using a first order approximation, we solve the equations of motion in the low
viscosity regime. This approach allows us to calculate the collision time, the
final velocity of each grain, and a coefficient of restitution that depends on
the relative velocity of the grains. We compare our analytic results with those
obtained by numerical integration of the equations of motion.
