  The motion of topological defects is an important feature of the dynamics of
all liquid crystals, and is especially conspicuous in active liquid crystals.
Understanding defect motion is a challenging theoretical problem, because the
dynamics of orientational order is coupled with backflow of the fluid, and
because a liquid crystal has several distinct viscosity coefficients. Here, we
suggest a coarse-grained, variational approach, which describes the motion of
defects as effective `particles.' For passive liquid crystals, the theory shows
how the drag depends on defect orientation, and shows the coupling between
translational and rotational motion. For active liquid crystals, the theory
provides an alternative way to describe motion induced by the activity
coefficient.
