系统地分析了有限维动力学中多项式类型的Lagrange函数所可能出现的四种情况, 并利用吴消元法和吴微分特征列法给出了判断折四种情况的两个算法. 利用这两个算法, 不用计算Hessian的秩, 就可以判别Euler-Lagrange方程是哪一种, 并得到相应的结果. 利用符号计算软件, 两个算法可以在计算机上实现.

In this paper, the polynomial type Lagrange equation of finite dimensional con-
strained dynamics is considered, and four possibilities of Euler-Lagrange equations
possibilities are analysed. Based on Wu elimination method and Wu differential
characteristic set method, two algorithms are presented for determining the four
possibilities. Using the two algorithms, without calculating the rank of Hessian
matrix, which case of the four possibilities of the Euler-Lagrange equations is de-
termined, and the corresponding result is obtained. On the symbolic computation
software platform, the two algorithms can be executed in computers.