Nonlocal constants of motion in Lagrangian Dynamics of any order

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