Local and global conserved quantities involving generalized operators

Abstract

Based on generalized operators, local conserved quantities, global conserved quantities and adiabatic invariants for the Lagrangian systems are studied. Firstly, Euler-Lagrange equations and transversality conditions are listed. Then local conserved quantities and global conserved quantities with the generalized operators are investigated. Thirdly, perturbation to Noether symmetry and adiabatic invariants are presented. Some special cases are discussed during this study. In the end, an example is given to illustrate the methods and results.