广义Hamilton系统的保结构算法

基于广义Hamilton系统微分方程解析解理论。给出了构造保持系统真解典则性的高阶显式积分格式的方法，并说明其可推广到广义Hamilton控制系统。该方法保持了原系统的几何定性特征，因而是稳定的。数值例子说明了算法的有效性。

An 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 numerical example and obtained results 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.