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.

A New Type of Conserved Quantity of Mei Symmetry for Lagrange Systems

“…(17) It is easy to verify that they satisfy Eqs. (10), so the infinitesimal generators (17) are Mei symmetrical for the system (16).…”

Noether conserved quantities and Lie point symmetries of difference Lagrange–Maxwell equations and lattices

“…Because of their applications the study of these systems is interesting, but the corresponding equations are generally difficult to solve due to the presence of nonlinear terms. In recent works on mechanico-electrical dynamical systems, authors have studied Lie symmetries and conserved quantities, [21−23] non-Noether symmetries and Lutzky conserved quantities, [24] momentumdependent symmetries and non-Noether conserved quantities, [25] and obtained the algebraic structure and Poisson's theory for these systems. [26] Besides this theoretical frame, it is interesting to build tools which can provide the numerical solutions and we have introduced difference techniques to obtain the variational principles and first-integrals for discrete mechanicoelectrical dynamical systems.…”

Unified symmetry of mechano-electrical systems with nonholonomic constraints

“…[16−25] In this paper, on the basis of Refs. [26][27][28][29][30], we study the unified symmetry of mechano-electrical systems with nonholonomic constraints and obtain the three kinds of conserved quantities mentioned above from the definition and the criterion of unified symmetry of the system.…”