The elliptic-regularization principle in Lagrangian mechanics

Abstract

We present a novel variational approach to Lagrangian mechanics based on elliptic regularization with respect to time. A class of parameter-dependent global-in-time minimization problems is presented and the convergence of the respective minimizers to the solution of the system of Lagrange's equations is ascertained. Moreover, we extend this perspective to mixed dissipative/nondissipative situations, present a finite time-horizon version of this approach, and provide related Gamma-convergence results. Finally, some discussion on corresponding time-discrete versions of the principle is presented.