  Within the framework of liquid crystal flows, the Qian & Sheng (QS) model for
Q-tensor dynamics is compared to the Volovik & Kats (VK) theory of biaxial
nematics by using Hamilton's variational principle. Under the assumption of
rotational dynamics for the Q-tensor, the variational principles underling the
two theories are equivalent and the conservative VK theory emerges as a
specialization of the QS model. Also, after presenting a micropolar variant of
the VK model, Rayleigh dissipation is included in the treatment. Finally, the
treatment is extended to account for nontrivial eigenvalue dynamics in the VK
model and this is done by considering the effect of scaling factors in the
evolution of the Q-tensor.
