  We study the magnetization dynamics of thin-film magnetic elements with
in-plane magnetization subject to a spin-current flowing perpendicular to the
film plane. We derive a reduced partial differential equation for the in-plane
magnetization angle in a weakly damped regime. We then apply this model to
study the experimentally relevant problem of switching of an elliptical element
when the spin-polarization has a component perpendicular to the film plane,
restricting the reduced model to a macrospin approximation. The macrospin
ordinary differential equation is treated analytically as a weakly damped
Hamiltonian system, and an orbit-averaging method is used to understand
transitions in solution behaviors in terms of a discrete dynamical system. The
predictions of our reduced model are compared to those of the full
Landau--Lifshitz--Gilbert--Slonczewski equation for a macrospin.
