or spherical particles in the presence of both inertia and HIs[@goddard_general_2012; @goddard_unification_2013], and hence also to several other DDFTs[@marconi_dynamic_2000; @archer_dynamical_2009; @archer_dynamical_2004; @espanol_derivation_2009; @goddard_overdamped_2012] which have neglected inertia or HIs or both. For orientable particles, neglecting inertial effects and HIs allows us to connect our DDFT with previous ones, recovering in particular the DDFTs derived by @rex_dynamical_2007 and @wittkowski_dynamical_2011. Concluding remarks along with a discussion of open problems are offered in Section \[sec:conclusions\].

Evolution equations {#sec:evolution-equations}
===================

Consider a closed system of $N$ identical, asymmetric colloidal particles with mass $m$ immersed in a fluid of $n\gg N$ identical bath particles with mass $m_b \ll m$. This mass separation plays a vital role in deriving the Brownian equations of motion governing colloidal dynamics via projection-operator techniques[@kirkwood_statistical_1946; @murphy_brownian_1972; @deutch_molecular_1971; @wilemski_derivation_1976; @ermak_brownian_1978; @grabert_microdynamics_1980; @darve_computing_2009] (see also Appendix \[app:projection-operator-tech\]). We start by describing the configuration state of the colloidal particles by the position vectors $\mathbf{r}^N=\{\mathbf{r}_1,\dots,\mathbf{r}_N\}$ for their centres of mass and the Eulerian angles ${\boldsymbol{\alpha}}^N=\{{\boldsymbol{\alpha}}_1,\dots,{\boldsymbol{\alpha}}_N\}$, with ${\boldsymbol{\alpha}}_i=(\theta_i,\phi_i,\chi_i)$ defined in the same manner as @condiff_brownian_1966 [@goldstein_classical_2002] or @jose_classical_2013. These angles characterise the orientation of principal-axes frame of the particles, $\mathfrak{B}$, relative to the space-fixed frame, $\mathfrak{S}$. We also denote the translational and angular momenta as ${\mathbf{p}}^N=\{{\mathbf{p}}_1,\dots,{\mathbf{p}}_N\}$ 