  We determine the trajectories of vortex singularities that arise after a
single vortex is broken by a discretely symmetric impulse in the context of
Bose-Einstein condensates in a harmonic trap. The dynamics of these
singularities are analyzed to determine the form of the imprinted motion. We
find that the symmetry-breaking process introduces two effective forces: a
repulsive harmonic force that causes the daughter trajectories to be ejected
from the parent singularity, and a Magnus force that introduces a torque about
the axis of symmetry. For the analytical non-interacting case we find that the
parent singularity is reconstructed from the daughter singularities after one
period of the trapping frequency. The interactions between singularities in the
weakly interacting system do not allow the parent vortex to be reconstructed.
Analytic trajectories were compared to the actual minima of the wavefunction,
showing less 0.5% error for impulse strength of (v=0.00005). We show that these
solutions are valid within the impulse regime for various impulse strengths
using numerical integration of the Gross-Pitaevskii equation. We also show that
the actual duration of the symmetry breaking potential does not significantly
change the dynamics of the system as long as the strength is below (v=0.0005).
