  Over the last few decades, classical density-functional theory (DFT) and its
dynamic extensions (DDFTs) have become powerful tools in the study of colloidal
fluids. Recently, previous DDFTs for spherically-symmetric particles have been
generalised to take into account both inertia and hydrodynamic interactions,
two effects which strongly influence non-equilibrium properties. The present
work further generalises this framework to systems of anisotropic particles.
Starting from the Liouville equation and utilising Zwanzig's
projection-operator techniques, we derive the kinetic equation for the Brownian
particle distribution function, and by averaging over all but one particle, a
DDFT equation is obtained. Whilst this equation has some similarities with
DDFTs for spherically-symmetric colloids, it involves a
translational-rotational coupling which affects the diffusivity of the
(asymmetric) particles. We further show that, in the overdamped (high friction)
limit, the DDFT is considerably simplified and is in agreement with a previous
DDFT for colloids with arbitrary shape particles.
