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In this paper we study the vanishing inertia and viscosity limit of a secondorder system set in an Euclidean space, driven by a possibly nonconvextime-dependent potential satisfying very general assumptions. By means of avariational approach, we show that the solutions of the singularly perturbedproblem converge to a curve of stationary points of the energy and characterizethe behavior of the limit evolution at jump times. At those times, the left andright limits of the evolution are connected by a finite number of heteroclinicsolutions to the unscaled equation.

A variational approach to the quasistatic limit of viscous dynamic evolutions in finite dimension