  We study the kinetic theory of driven granular gases, taking into account
both translational and rotational degrees of freedom. We obtain the high-energy
tail of the stationary bivariate energy distribution, depending on the total
energy E and the ratio x=sqrt{E_w/E} of rotational energy E_w to total energy.
Extremely energetic particles have a unique and well-defined distribution f(x)
which has several remarkable features: x is not uniformly distributed as in
molecular gases; f(x) is not smooth but has multiple singularities. The latter
behavior is sensitive to material properties such as the collision parameters,
the moment of inertia and the collision rate. Interestingly, there are
preferred ratios of rotational-to-total energy. In general, f(x) is strongly
correlated with energy and the deviations from a uniform distribution grow with
energy. We also solve for the energy distribution of freely cooling Maxwell
Molecules and find qualitatively similar behavior.
