Noether-type theory for discrete mechanico-electrical dynamical systems with nonregular lattices

We investigate Noether symmetries and conservation laws of the discrete mechanico-electrical systems with nonregular lattices. The operators of discrete transformation and discrete differentiation to the right and left are introduced for the systems. Based on the invariance of discrete Hamilton action on nonregular lattices of the systems with the dissipation forces under the infinitesimal transformations with respect to the time, generalized coordinates and generalized charge quantities, we work out the discrete analog of the generalized variational formula. From this formula we derive the discrete analog of generalized Noether-type identity, and then we present the generalized quasi-extremal equations and properties of these equations for the systems. We also obtain the discrete analog of Noether-type conserved laws and the discrete analog of generalized Noether theorems for the systems. Finally we use an example to illustrate these results.