  The dynamical properties of a tracer or impurity particle immersed in a host
gas of inelastic and rough hard spheres in the homogeneous cooling state is
studied. Specifically, the breakdown of energy equipartition as characterized
by the tracer/host ratios of translational and rotational temperatures is
analyzed by exploring a wide spectrum of values of the control parameters of
the system (masses, moments of inertia, sizes, and coefficients of
restitution). Three complementary approaches are considered. On the theoretical
side, the Boltzmann and Boltzmann--Lorentz equations (both assuming the
molecular chaos ansatz) are solved by means of a multitemperature Maxwellian
approximation for the velocity distribution functions. This allows us to obtain
explicit analytical expressions for the temperature ratios. On the
computational side, two different techniques are used. First, the kinetic
equations are numerically solved by the direct simulation Monte Carlo (DSMC)
method. Second, molecular dynamics simulations for dilute gases are performed.
Comparison between theory and simulations shows a general good agreement. This
means that (i) the impact of the molecular chaos ansatz on the temperature
ratios is not significant (except at high inelasticities and/or big impurities)
and (ii) the simple Maxwellian approximation yields quite reliable predictions.
