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arXiv · 2104.14793

Nonlocal constants of motion in Lagrangian Dynamics of any order

Gianluca Gorni·Mattia Scomparin·Gaetano Zampieri
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Abstract

We describe a recipe to generate "nonlocal" constants of motion for ODE Lagrangian systems. As a sample application, we recall a nonlocal constant of motion for dissipative mechanical systems, from which we can deduce global existence and estimates of solutions under fairly general assumptions. Then we review a generalization to Euler-Lagrange ODEs of order higher than two, leading to first integrals for the Pais-Uhlenbeck oscillator and other systems. Future developments may include adaptations of the theory to Euler-Lagrange PDEs.

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Gianluca Gorni, Mattia Scomparin, Gaetano Zampieri. 2021-04-30. Nonlocal constants of motion in Lagrangian Dynamics of any order. https://arxiv.org/abs/2104.14793

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