Noether symmetries of discrete nonholonomic dynamical systems

Abstract

In this letter, we investigate Noether symmetries and conservation laws of discrete dynamical systems on an uniform lattice with the nonholonomic constraints. Based on the quasi-invariance of discrete Hamiltonian action of the systems under the infinitesimal transformation with respect to the time and generalized coordinates, we give the discrete analogue of generalized variational formula of the systems. From this formula we derive the discrete analogue of generalized Noether-type identity, and then we present the generalized quasi-extremal equations of the systems. We also obtain the discrete analogue of Noether theorems and the discrete analogue of Noether conservation laws of the systems. Finally, an example is discussed to illustrate these results.