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arXiv · 2304.15007

Newton's second law as limit of variational problems

Edoardo Mainini·Danilo Percivale
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Abstract

We show that the solution of the Cauchy problem for the classical ode $m \mathbf y''=\mathbf f$ 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.

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Edoardo Mainini, Danilo Percivale. 2023-04-28. Newton's second law as limit of variational problems. https://doi.org/10.1186/s13662-023-03766-4

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