| 张素英,邓子辰.广义Hamilton系统的保结构算法[J].计算力学学报,2005,22(1):47~50 |
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| 广义Hamilton系统的保结构算法 |
| An algorithm for preserving structure of generalized Hamilton system |
| 修订日期：2002-04-14 |
| DOI：10.7511/jslx20051010 |
| 中文关键词: 广义Hamilton系统 广义Poisson括号结构 典则变换 |
| 英文关键词:generalized Hamilton system,generalized Poisson bracket structure,canonical transform |
| 基金项目:国家自然科学基金(10372084，10472059)，高校博士点基金 (2 0 0 1 0 6 990 1 6 )，霍英东青年教师基金(71 0 0 5)，航空科学基金 (0 0 B53 0 0 6 )，陕西省自然科学基金 (2 0 0 2 A1 7)，大连理工大学工业装备结构分析国家重点实验室开放基金资助项目 |
| 张素英 邓子辰 |
| [1]西北工业大学工程力学系,陕西西安,710072 [2]西北工业大学工程力学系,陕西西安,710072／／大连理工大学工业装备结构分析国家重点实验室,辽宁大连,116024 |
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| 中文摘要: |
| 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。 |
| 英文摘要: |
| 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. |
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