摘要
Poisson流形是研究广义 Hamilton系统的恰当几何结构。本文在 Poisson流形上讨论广义Hamilton系统的保结构的数值解法 ,为广义 Hamilton系统的数值计算提供了理论基础。文中通过算例证明了算法的保结构性和稳定性 ,同时说明了该算法可以推广到广义 Hamilton控制系统。
Feng, in Ref. 2, proposed an algorithm for preserving the canonical character of Hamiltonian system, thus ensuring that numerical iteration lead to correct results. We propose an algorithm for preserving the canonical character of generalized Hamiltonian system. We preserve its canonical character by preserving its generalized Poisson bracket structure. Section 2 mentions the research results of Ref. 4 on conditions that must be strictly observed for preserving generalized Poisson bracket structure. Section 3 gives our algorithm, which is an explicit scheme of second order, and discusses how we introduce embedding cycle in our algorithm to make its precision higher. Section 4 gives a numerical example and the numerical results given in Table 1 show preliminarily that our algorithm is feasible.
出处
《西北工业大学学报》
EI
CAS
CSCD
北大核心
2002年第4期625-628,共4页
Journal of Northwestern Polytechnical University
基金
国家自然科学基金 (19872 0 5 7)
高校博士点基金 (2 0 0 10 6 990 16 )
霍英东青年教师基金 (710 0 5 )
航空科学基金 (0 0 B5 30 0 6 )
陕西省自然科学基金 (2 0 0 2 A17)
大连理工大学工业装备结构分析国家实验室开放基金