English

Newton's second law as limit of variational problems

Analysis of PDEs 2023-05-01 v1

Abstract

We show that the solution of the Cauchy problem for the classical ode my=fm \mathbf y''=\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.

Keywords

Cite

@article{arxiv.2304.15007,
  title  = {Newton's second law as limit of variational problems},
  author = {Edoardo Mainini and Danilo Percivale},
  journal= {arXiv preprint arXiv:2304.15007},
  year   = {2023}
}