  We study the Thiele equation for current-induced motion in a skyrmion lattice
through two soluble models of the pinning potential. Comprised by a Magnus
term, a dissipative term and a pinning force, Thiele's equation resembles
Newton's law but in virtue of the topological character of the first two, it
differs significantly from Newtonian mechanics and because the Magnus force is
dominant, unlike its mechanical counterpart, the Coriolis force, skyrmion
trajectories do not necessarily have mechanical counterparts. This is important
if we are to understand skykrmion dynamics and tap into its potential for
data-storage technology. We identify a pinning threshold velocity for the
one-dimensional potential and for a two-dimensional potential we find a pinning
point and the skyrmion trajectories toward the point are spirals whose
frequency (compare Kepler's second law) and amplitude decay depends only on the
Gilbert constant and potential at the pinning point.
