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
2022-01-01
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.File in questo prodotto:
File | Dimensione | Formato | |
---|---|---|---|
Padiff-GSZ.pdf
accesso aperto
Tipologia:
Versione dell'editore
Licenza:
Creative commons
Dimensione
368.8 kB
Formato
Adobe PDF
|
368.8 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.