带约束动力学辛算法的符号计算

THE SYMBOLIC COMPUTATION OF SYMPLECTIC ALGORITHM IN CONSTRAINED DYNAMICS

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.

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 type Euler-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.