吴消元法在Lagrange和Hamilton方程中的应用

基金项目: 国家自然科学基金资助项目(10401021);中国科学院研究生院科研启动基金资助项目(M3002)

Application of Wu Elimination Method to Constrained Dynamics

Department of Mathematics, Graduate University, Chinese Academy of Sciences, Beijing 100049, P. R. China;

摘要: 主要借鉴吴消元法，研究带约束动力学中多项式类型Lagrange方程和Hamilton方程，提出了一种求约束的新算法．与以前算法相比，新算法无需求Hessian矩阵的秩，无需判定方程的线性相关性，从而大为减少了计算步骤，且计算更为简单．此外，计算过程中膨胀较小，且多数情形下无膨胀．利用符号计算软件，新算法可在计算机上实现．
- Hamilton系统 /
- 约束 /
- 特征列 /
- Hessian矩阵
Abstract: The polynomial type Lagrange equation and Hamilton equation of finite dimensional constrained dynamics are considered. A new algorithm was presented for solving constraints based on Wu elimination method. The new algorithm does not need to calculate the rank of Hessian matrix and determine the linear dependence of equations, so the steps of calculation decrease greatly. In addition, the expanding of expression occurring in the computing process is smaller. Using the symbolic computation software platform, the new algorithm can be executed in computers.
- Hamilton system /
- constrained dynamics /
- characteristic chain /
- Hessian matrix

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