Newton's second law as limit of variational problems

Abstract

We show that the solution of the Cauchy problem for the classical ode $m{\mathbf{y}}^{\prime \prime }=\mathbf{f}$ can be obtained as limit of minimizers of exponentially weighted convex variational integrals. This complements the known results about weighted inertia-energy approach to Lagrangian mechanics and hyperbolic equations.