Momentum-dependent symmetries and non-Noether conserved quantities for mechanico-electrical systems

Abstract

The Hamiltonian canonical equation of the systems, the definition, criterion, structure equation and conserved quantities of momentum-dependent symmetries for Lagrange-Maxwell mechanico-electrical systems were presented. This work shows that the function ψ in the structure equation is only an invariant on the symmetry group. A new method to deduce conserved quantities of mechanico-electrical systems is obtained. An example is designed to illustrate these results.