Composite variational principles, added variables, and constants of motion
It is shown that any second order differential system admits a variational formulation via the introduction of suitable additional variables. The new variables are related to the existence of invariant 1- forms and to solutions for the adjoint of the equations of variation of the given system. The connections among invariant forms, constants of motion, and infinitesimal invariance transformations are then discussed in some detail.
scientific article; zbMATH DE number 3983671
scientific article