The Lie symmetrical non-Noether conserved quantity of holonomic Hamiltonian system

In this paper, we study the Lie symmetrical non-Noether conserved quantity of a holonomic Hamiltonian system under the general infinitesimal transformations of groups. Firstly, we establish the determining equations of Lie symmetry of the system. Secondly, the Lie symmetrical non-Noether conserved quantity of the system is deduced. Finally, an example is given to illustrate the application of the result.