Discrete variational principle and first integrals for Lagrange–Maxwell mechanico-electrical systems

Abstract

This paper presents a discrete variational principle and a method to build first-integrals for finite dimensional Lagrange–Maxwell mechanico-electrical systems with nonconservative forces and a dissipation function. The discrete variational principle and the corresponding Euler–Lagrange equations are derived from a discrete action associated to these systems. The first-integrals are obtained by introducing the infinitesimal transformation with respect to the generalized coordinates and electric quantities of the systems. This work also extends discrete Noether symmetries to mechanico-electrical dynamical systems. A practical example is presented to illustrate the results.