Nonlocal constants of motion in Lagrangian Dynamics of any order
Dynamical Systems
2021-05-07 v2 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.2104.14793,
title = {Nonlocal constants of motion in Lagrangian Dynamics of any order},
author = {Gianluca Gorni and Mattia Scomparin and Gaetano Zampieri},
journal= {arXiv preprint arXiv:2104.14793},
year = {2021}
}