We show that the solution of Cauchy problem for the classical ODE my″= 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.
Newton’s second law as limit of variational problems
Percivale D.;Mainini E.
2023-01-01
Abstract
We show that the solution of Cauchy problem for the classical ODE my″= 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.
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