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.

Nonlocal constants of motion in Lagrangian Dynamics of any order

Zampieri, Gaetano
Membro del Collaboration Group
2022

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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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11562/1057255
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