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| SYMPLECTIC STRUCTURE OF POISSON SYSTEM | |
| 作者姓名： | 孙建强 马中骐 田益民 秦孟兆 GU Yuan-xian |
| 作者单位： | [1]Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100039, P. R. China [2]Institute of Applied Physics and Computational Mathematics, Beijing 100088, P. R. China [3]Institute of Software, Chinese Academy of Sciences, Beijing 100080, P. R. China [4]Institute of Computational Mathematics, Chinese Academy of Sciences, Beijing 100080, P. R. China [5]不详, Chinese Academy of Sciences, Beijing 100080, P. R. China |
| 基金项目： | Project supported by the National Natural Science Foundation of China （Nos. 10401033, 90103003 and 10471145） |
| 摘 要： | When the Poisson matrix of Poisson system is non-constant, classical symplectic methods, such as symplectic Runge-Kutta method, generating function method, cannot preserve the Poisson structure. The non-constant Poisson structure was transformed into the symplectic structure by the nonlinear transform.Arbitrary order symplectic method was applied to the transformed Poisson system. The Euler equation of the free rigid body problem was transformed into the symplectic structure and computed by the midpoint scheme. Numerical results show the effectiveness of the nonlinear transform. |
| 关 键 词： | Poisson系统 对称结构 非线性传播 刚性体 Poisson结构 |
| 文章编号： | 0253-4827（2005）11-1484-07 |
| 收稿时间： | 2004-07-15 |
| 修稿时间： | 2005-06-16 |
Symplectic structure of poisson system |
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| Jian-qiang Sun,Zhong-qi Ma,Yi-min Tian,Meng-zhao Qin.SYMPLECTIC STRUCTURE OF POISSON SYSTEM[J].Applied Mathematics and Mechanics(English Edition),2005,26(11):1484-1490. | |
| Authors: | Jian-qiang Sun Zhong-qi Ma Yi-min Tian Meng-zhao Qin |
| Institution: | 1. Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, 100039, P. R. China 2. Institute of Applied Physics and Computational Mathematics, Beijing, 100088, P. R. China 3. Institute of Software, Chinese Academy of Sciences, Beijing, 100080, P. R. China 4. Institute of Computational Mathematics, Chinese Academy of Sciences, Beijing, 100080, P. R. China |
| Abstract: | When the Poisson matrix of Poisson system is non-constant, classical symplectic methods, such as symplectic Runge-Kutta method, generating function method, cannot preserve the Poisson structure. The non-constant Poisson structure was transformed into the symplectic structure by the nonlinear transform. Arbitrary order symplectic method was applied to the transformed Poisson system. The Euler equation of the free rigid body problem was transformed into the symplectic structure and computed by the mid-point scheme. Numerical results show the effectiveness of the nonlinear transform. |
| Keywords: | Poisson system nonlinear transformation symplectic method rigid body problem |
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