  We derive the frequency of precession and conditions for stability for a
quantized vortex in a single-component and a two-component Bose-Einstein
condensate. The frequency of precession is proportional to the gradient of the
free energy with respect to displacement of the vortex core. In a two-component
system, it is possible to achieve a local minimum in the free energy at the
center of the trap. The presence of such a minimum implies the existence of a
region of energetic stability where the vortex cannot escape and where one may
be able to generate a persistent current.
