Noether Symmetry and First Integral of Discrete Nonconservative and Nonholonimic Hamiltoinian System

Abstract

The letter focuses on studying Noether symmetry and conserved quantity of discrete nonconservative and nonholonomic Hamiltonian system. Firstly, the discrete Hamiltonian canonical equations and discrete energy equations of nonconservative and nonholonomic Hamiltonian systems are derived with discrete Hamiltonian action. Secondly, based on the quasi-invariance of discrete Hamiltonian action and equation of lattice under the infinitesimal transformation with respect to time, generalized coordinates and generalized momentums, the discrete analogue of Noether’s identity and determining equation of lattice are obtained for the systems. Thirdly, the discrete analogues of Noether’s theorems and conserved quantities of the systems are presented. Finally, one example is discussed to illustrate the application of the results.