  In this paper we study the vanishing inertia and viscosity limit of a second
order system set in an Euclidean space, driven by a possibly nonconvex
time-dependent potential satisfying very general assumptions. By means of a
variational approach, we show that the solutions of the singularly perturbed
problem converge to a curve of stationary points of the energy and characterize
the behavior of the limit evolution at jump times. At those times, the left and
right limits of the evolution are connected by a finite number of heteroclinic
solutions to the unscaled equation.
