Symmetry theories for canonicalized equations of constrained Hamiltonian system

In this paper, we give a new method to investigate Noether and Lie symmetries of constrained Hamiltonian system. Firstly, we study the canonicalization of constrained Hamiltonian system. Through variable transformation, the old variables are replaced by the new variables, and at this point, the motion equations for the constrained Hamiltonian system have been canonicalized. Then, we follow the usual symmetry method for the constrained mechanical system, and the Noether and Lie symmetries of constrained Hamiltonian system are given. Finally, three examples are presented to illustrate the application of the results.