LIE SYMMETRIES AND CONSERVED QUANTITIES OF DISCRETE CONSTRAINED HAMILTON SYSTEMS

In this paper, the Lie symmetry theory of discrete singular systems is studied in phase space. Firstly, the discrete canonical equations and the energy evolution equations of the constrained Hamilton systems are established based on the discrete difference variational principle. Secondly, the Lie point transfoimation of discrete group is applied to the difference equations and constraint restriction, and the Lie symmetry determination equations of the discrete constrained Hamilton systems are obtained; Meanwhile, the Lie symmetries of singular systems lead to the discrete Noehter type conserved quantities when the structure condition equations (discrete Noether identity) are established. Finally, an example is given to illustrate the application, the results show that the conservative constrained Hamilton systems also have the discrete energy conservation.