定常Chetaev型非完整系统的组合梯度表示

Combined Gradient Representations of Stationary Nonholonomic System of Chetaev's Type

提出了6类组合梯度系统的定义,分别给出了这6类组合梯度系统的微分方程,并进一步研究了定常Chetaev型非完整系统的组合梯度表示.得到非完整系统的相应完整系统成为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组合梯度系统.最后利用组合梯度系统的性质来研究系统的稳定性.举例说明结果应用.

The six kinds of combined gradient systems were proposed and the differential equations of the six kinds of combined gradient systems were given respectively. Further, the combined gradient representations of a stationary nonholonomic system of Chetaev＇s type were studied. The conditions under which the corresponding holonomic system of the nonholonomic system can be considered as a kind of the combined gradient systems were obtained, so the stationary nonholonomic system of Chetaev＇s type was transformed into each combined gradient systems. Finally, the characteristic of the combined gradient systems can be used to study the stability of the system. Some examples were given to illustrate the application of the results.