| 带约束动力学辛算法的符号计算 |
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| 引用本文： | 贾屹峰,陈玉福. 带约束动力学辛算法的符号计算[J]. 系统科学与数学, 2010, 30(9): 1175-1184 |
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| 作者姓名： | 贾屹峰 陈玉福 |
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| 作者单位： | 1. 中国劳动关系学院基础部,北京,100048
2. 中国科学院研究生院数学科学学院,北京,100049 |
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| 基金项目： | 中国劳动关系学院院级课题孤立子中的符号计算研究 |
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| 摘 要： | 首先对带约束动力学中的辛算法作了改进,利用吴消元法求解多项式类型Euler-Lagrange方程.在辛算法的基础上,根据线性方程组理论和相容条件提出了一个求解约束的新算法.新算法的推导过程比辛算法严格,而且计算也比辛算法简单,并且多项式类型的Euler-Lagrange仍可以用吴消元法求解.另外,对于某些非多项式类型的Euler-Lagrange方程,可以先化为多项式类型,再用吴消元法求解.利用符号计算软件,上述算法都可以在计算机上实现.
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| 关 键 词： | 约束 特征列 辛矩阵 Euler-Lagrange方程. |
| 收稿时间： | 2010-02-10 |
THE SYMBOLIC COMPUTATION OF SYMPLECTIC ALGORITHM IN CONSTRAINED DYNAMICS |
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| JIA Yifeng,CHEN Yufu. THE SYMBOLIC COMPUTATION OF SYMPLECTIC ALGORITHM IN CONSTRAINED DYNAMICS[J]. Journal of Systems Science and Mathematical Sciences, 2010, 30(9): 1175-1184 |
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| Authors: | JIA Yifeng CHEN Yufu |
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| Affiliation: | (1)Basic Department, China Institute of Industrial Relations, 100048;(2)School of Mathematical Sciences, Graduate University Chinese Academy of Sciences, 100049 |
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| Abstract: | In this paper, firstly, the Symplectic algorithm in constrained dynamics is improved; the Euler-Lagrange equations are solved by Wu eliminate method. Based on Symplectic algorithm, according to the theory of linear equation system and consistent conditions, a new algorithm is presented. The deduction of new algorithm is more rigorous than the Symplectic algorithm, the process of computation is simpler the Symplectic algorithm, and the polynomial typeEuler-Lagrange equation can be also solved with Wu eliminate method. In addition, some non-polynomial type Euler-Lagrange equation can be solved with Wu eliminate. By using the symbolic software, the above algorithms can be executed in computers. |
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| Keywords: | Constraints characteristic set symplectic matrix Euler-Lagrange equation. |
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