一阶非线性非完整系统Routh方程的不定乘子及约束反力

在工程实际中,求解约束反力往往是必要的。在控制系统中,要求实现的运动规律可以看作约束,而约束反力就是必须作用的控制力。Routh方程既能求解运动又能求解约束反力。约束反力包含在不定乘子中,而不定乘子出现在每个方程中。本文引进伪速度将决定运动的方程和不定乘子从Routh方程中分离开来,得到每个不定乘子的表达式;并讨论了一阶非线性非完整系统,一阶线性非完整系统和完整系统的约束反力,以及冲击约束反力。

THE INDETERMINATE MULTIPERS AND CONSTRAINED FORCES OF ROUTH'S EQUATION OF FIRST ORDER NONLINEAR NONHOLONOMIC SYSTEM

In practical engineering, it is usually necessary to find out the constrained force. The moving rule required to realize in controlling system is considered to be a constraint and the constrained forces are controlling forces having to act on the system. Both the movement and the constrained forces may be solved by Routh's equation. The constrained forces are contained in the inderminate multipers, which appear in every equation. Introducing quasi-velosity in this paper, the equation to determine the movement and the ndeterminate multipers may be separated from Routh's equation, thus obtaining the expression of every indeterminate multiper. The constia ned forces and also the impulsive constrained forces of first order linear and nonlinear nonholonomic systems and holonomic systems are discussed.