研究判定定常Chetaev型非完整系统稳定性的三重组合梯度方法. 首先,分别给出4类基本梯度系统和4类三重组合梯度系统的定义和微分方程；其次,得到非完整系统的相应完整系统成为三重组合梯度系统的条件,从而将定常Chetaev型非完整系统化成各类三重组合梯度系统；最后,利用三重组合梯度系统的性质来研究系统的稳定性. 举例说明结果的应用.
A triple combined gradient method was studied to determine the stability of nonholonomic systems of constant Chetaev′s type. Firstly,the definitions and differential equations of four classes of basic gradient systems and four classes of triple combined gradient systems were given. Secondly,the conditions,under which the corresponding holonomic systems of nonholonomic systems become triple combined gradient systems,were obtained. Therefore,the constant Chetaev nonholonomic systems can be transformed into various triple combined gradient systems. Finally,the stability of the system is studied by using the properties of the triple combined gradient system. The applications of this method were illustrated by four examples.