| Hamilton系统的保辛 守恒积分算法 |
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| 引用本文： | 高强,钟万勰.Hamilton系统的保辛 守恒积分算法[J].动力学与控制学报,2009,7(3):193-199. |
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| 作者姓名： | 高强 钟万勰 |
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| 作者单位： | 大连理工大学工程力学系,工业装备结构分析国家重点实验室,大连,116023 |
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| 基金项目： | 自然科学基金，辽宁省博士启动基金，大连理工大学青年教师培养基金和大连理工大学理学基金资助 |
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| 摘 要： | 给出了Hamilton系统基于辛矩阵乘法的显式时不变正则变换和时变正则变换．引入含参变量的近似Hamilton系统，并以近似Hamilton系统为基础进行辛矩阵乘法的正则变换．正则变换保证了数值积分的保辛性质，而通过调整引入的参变量可保证能量在积分格点上守恒．实现了Hamilton系统即保辛又保能量的算法．
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| 关 键 词： | 保辛 能量守恒 参变量 正则变换 |
| 收稿时间： | 2009/1/31 0:00:00 |
| 修稿时间： | 2009/3/13 0:00:00 |
The symplectic and energy preserving method for the integration of hamilton system |
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| Gao Qiang and Zhong Wanxie.The symplectic and energy preserving method for the integration of hamilton system[J].Journal of Dynamics and Control,2009,7(3):193-199. |
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| Authors: | Gao Qiang and Zhong Wanxie |
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| Affiliation: | Gao Qlang Zhong Wanxie (Department of Engineering Mechanics, State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian 116023, China) |
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| Abstract: | The time independent and time dependent canonical transformations based on the multiplication of symplectic matrix were given for Hamilton system. The approximate Hamilton system with parametric variable was introduced, and the canonical transformation was performed based on this approximate Hamilton system. The symplectic preserving property of the numerical methods was guaranteed by the canonical transformation, and the energy in the integration time can be adjusted to be constant by changing the parametric variable. So the symplectic and energy preserving method for Hamilton system was obtained. |
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| Keywords: | symplectic preserving energy preserving parametric variable canonical transformation |
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