  Free cooling of granular materials is analyzed on the basis of a
pseudo-Liouville operator. Exchange of translational and rotational energy
requires surface roughness for spherical grains, but occurs for non-spherical
grains, like needles, even if they are perfectly smooth. Based on the
assumption of a homogeneous cooling state, we derive an approximate analytical
theory. It predicts that cooling of both rough spheres and smooth needles
proceeds in two stages: An exponentially fast decay to a state with stationary
ratio of translational and rotational energy and a subsequent algebraic decay
of the total energy. These results are confirmed by simulations for large
systems of moderate density. For higher densities, we observe deviations from
the homogeneous state as well as large-scale structures in the velocity field.
We study non-Gaussian distributions of the momenta perturbatively and observe a
breakdown of the expansion for particular values of surface roughness and
normal restitution.
