非线性非完整系统相对平衡状态流形的稳定性

本文研究非线性非完整系统相对于非惯性系平衡状态流形上的稳定性问题。首先，将非线性非完整系统的相对运动问题当作一个有条件的完整系统问题来处理。其次，当系统存在平衡状态时，用一次近似方程来研究其相应完整系统平衡态流形的稳定性问题；如果一次近似方程是常系数的，其特征方程不可避免地会出现零根，零根的数目等于非完整约束方程的数目与非完整系统平衡状态流形的维数之和；将这些零根简单地去掉，就可据其它根是否有负实部来判断稳定性。最后，举例说明此方法的应用。

THE STABILITY OF THE RELATIVE EQUILIBRIUM STATE MANIFOLD OF NONLINEAR NONHOLONOMIC SYSTEMS

In this paper the stability problems of the relative equilibrium state manifold of nonlinear systems with nonholonomic constraints in a noninertial reference frame have been studied from the modern differential geometry point of view. The relative motion of nonlinear nonholonomic systems can be regarded as a problem of conditional holonomic systems. If an equilibrium state exists in nonlinear nonholonomic systems, we may study the stability of the equilibrium state manifold of the corresponding holonomic systems by using the linear approximate equation. If the linear approximate equation has constant coeficients, some roots of its characteristic equation must be equal to zero, so that we may judge the stability of the system from the properties of the nonzero roots of the characteristic equation, i. e. whether the real parts of the nonzero roots are negative or non negative. An exemple is given in the last section.