hard sphere systems[@goddard_unification_2013], mixtures[@goddard_multi-species_2013], thermodynamic phase transitions such as nucleation and spinodal decomposition[@van_teeffelen_colloidal_2008; @lutsko_dynamical_2012] to the calculation of the van Hove distribution function for Brownian hard spheres[@hopkins_van_2010] and crystallization[@neuhaus_density_2014].

DDFTs have been derived for both the overdamped and inertial regimes and although they were initially applied to spherically-symmetric colloids, they have also been generalised to systems where both orientational and translational motions of particles are taken into account, either under weak[@rex_dynamical_2007] or strong[@wittkowski_dynamical_2011] coupling between the two motions. However, these generalisations are restricted to the overdamped regime and neglect HIs. The main goal of the present study is precisely to formulate a DDFT for orientable particles to include both inertia and HIs. Our methodology follows closely the momentum-moments approach adopted by @archer_dynamical_2009 to obtain a DDFT for spherically-symmetric colloidal particles with inertia and also by @goddard_general_2012[@goddard_general_2012; @goddard_unification_2013] to include both inertia and HIs in this DDFT.

In Section \[sec:evolution-equations\] we introduce the equations of motion for a system of $N$ interacting orientable colloidal particles immersed in a thermal bath. Analogous to the spherically-symmetric case, these equations are the LEs for the phase-space coordinates: positions, Eulerian angles, linear and angular (also referred to as rotational) momenta. These equations have already been 