摘要
本文对Lagrange力学逆问题进行了探讨.在文献[1]的基础上,对牛顿系统的基本形式、运动形式及在一维系统、一阶方程组等特殊情形下的自伴随条件作了研究.并且结合Ⅰ程实际中的问题,应用构造Lagrange函数的Engels第一方法,得到了一个一阶方程组和一个二维非保守非线性系统的Lagrange函数,为获得最佳控制提供了必要的依据.
This paper probes into the converse problem of Lagrange mechanics.On the basis of reference [1], the paper investigates the basic pattern and motion regulation of Newton system, and the selfadjoint condition in the special cases of one dimension systems and equation combination of one degree.
The paper applies the Engels's first method for constructing Lagrangian function to engineering problems, and gets a Lagrangian function of one degree equation combination and two dimension, nonconservative and nonlinear system.It provides scientific basis for optimum control.
关键词
力学逆问题
自伴随条件
拉格朗日
converse problem of lagrange mechanics
selfadjoint condition
Engels's first method
