Algorithm for preserving structure of generalized Hamilton system

For generalized Hamilton system and generalized Hamilton control system, based on the analytical theory of the differential equation for generalized Hamilton system, a high order explicit integration algorithm that can preserve canonical character of system real solution is proposed, which can be extended to the generalized Hamilton control system. Firstly, the definitions of Poisson bracket structure and generalized Hamilton system are given, then a concrete computational process is constructed, in which an algorithm for preserving structure of generalized Hamilton system is established that can preserve the geometry characters of the original system and is stable for the numerical computation. The results of a numerical example show that the proposed preserving structure method is effective for generalized Hamilton system. The work of this paper will provide a new way for the further studies of Hamilton dynamic system.