  We investigate the vortex excitations induced by a spin-polarized current in
a magnetic nanopillar by means of micromagnetic simulations and analytical
calculations. Damped motion, stationary vortex rotation and the switching of
the vortex core are successively observed for increasing values of the current.
We demonstrate that even for small amplitude of the vortex motion, the
analytical description based the classical Thiele approach can yield
quantitatively and qualitatively unsound results. We suggest and validate a new
analytical technique based on the calculation of the energy dissipation.
