We solve the Smoluchowski equation for steady state solutions of rigid nematic
polymers and suspensions under imposed elongational flow, magnetic or electric fields, respectively.
Under the three imposed fields, we show that (1) the Smoluchowski equation can be cast into a
generic form, (2) the external field must parallel to one of the eigenvectors of the second moment
tensor in steady states, and (3) the steady state solution of the Smoluchowski equation (probability
density function or simply pdf) is of the Boltzmann type parameterized by material parameters and
two order parameters governed by two algebraic-integral equations. Then, we present a complete
bifurcation diagram of the order parameters with respect to the material parameters by solving
the algebraic-integral equations. The stability of the pdf solutions is inferred from the minimum
of the free energy density. The solution method is extended to dilute solutions of dipolar, rigid
nematic polymers under an imposed electric field. The first moment of the steady state pdf is shown
to be parallel to the external field direction at sufficiently strong permanent dipole or relatively
weak dipole-dipole interaction. In this case, the steady solution of the Smoluchowski equation is
parameterized by one order parameter and material parameters in the Boltzmann form. Otherwise,
the first moment is not necessarily parallel to the external field direction.