  We present an analytical model to account for the inertial dynamics of a
magnetic vortex. The model is based on a deformation of the core profile based
on the D\"oring kinetic field, whereby the deformation amplitudes are promoted
to dynamical variables in a collective-coordinate approach that provides a
natural extension to the Thiele model. This extended model accurately describes
complex transients due to inertial effects and the variation of the effective
mass with velocity. The model also provides a quantitative description of the
inertial dynamics leading up to vortex core reversal, which is analogous to the
Walker transition in domain wall dynamics.
