A New Approach to Constants of the Motion and the Helmholtz Conditions

Abstract

Based on the Helmholtz conditions for the existence of a Lagrangian, we discuss a new approach to constants of the motion associated with continuous symmetries of the equations of motion . It is shown that the constants so determined vanish whenever the symmetry group is related to actual invariance of the Lagrangian (whose existence is guaranteed by the validity of the Helmholtz conditions) ; in which case , however , we have available the classical Noether invariants for constants of the motion. Copyright © www.iiste.org

Keywords: : Helmholtz conditions, Conservation laws, Symmetry