  We introduce a characterization of disclination lines in three dimensional
nematic liquid crystals as a tensor quantity related to the so called rotation
vector around the line. This quantity is expressed in terms of the nematic
tensor order parameter $\mathbf{Q}$, and shown to decompose as a dyad involving
the tangent vector to the disclination line and the rotation vector. Further,
we derive a kinematic law for the velocity of disclination lines by connecting
this tensor to a topological charge density as in the Halperin-Mazenko
description of defects in vector models. Using this framework, analytical
predictions for the velocity of interacting line disclinations and of
self-annihilating disclination loops are given and confirmed through numerical
computation.
