Kinetic equations for smooth granular systems

In the present work we derive kinetic equations for the rarified granular gas from the Fokker-Planck equation that describes the time evolution of the reduced distribution function for the translational granular degrees of freedom. We obtain the explicit form for the inelastic dissipation term and calculate the time evolution of the granular temperature for the homogeneous granular gas. Our result differs from that in which the coefficient of restitution is assumed to be velocity independent.