Mei symmetry leading to Mei conserved quantity of generalized Hamiltonian system

For a generalized Hamiltonian system, Met conserved quantity derived by using Mei symmetry is studied. First, the definition,the criterion and the determining equations of Mei symmetry of generalized Hamiltonian system are given under infinitesimal transformations of group. Second, the conditions and the forms for existence of Mei conserved quantity are directly obtained by using the Mei symmetry of the system. Then, the theorem for existence of Mei conserved quantity of generalized Hamiltonian system with additional terms is given. Finally, a new three-dimensional generalized Hamiltonian system and the plane motion of the three vortices of three-body problem are studied by using the method presented in the paper.