Work

Newton’s second law as limit of variational problems

Year: 2023

Type: article

Abstract: We show that the solution of Cauchy problem for the classical ODE $m \mathbf {y}''=\mathbf {f}$ m y ″ = f can be obtained as the 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.

Source: Advances in Continuous and Discrete Models

DOI: 10.1186/s13662-023-03766-4

Authors: Danilo Percivale, Edoardo Mainini

Institution: University of Genoa

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $1,790

Funder: Ministero dell’Istruzione, dell’Università e della Ricerca