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 引用本文: 陈向炜, 曹秋鹏, 梅凤翔. 切塔耶夫型非完整系统的广义梯度表示[J]. 力学学报, 2016, 48(3): 684-691.
Chen Xiangwei, Cao Qiupeng, Mei Fengxiang. GENERALIZED GRADIENT REPRESENTATION OF NONHOLONOMIC SYSTEM OF CHETAEV'S TYPE[J]. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(3): 684-691.
 Citation: Chen Xiangwei, Cao Qiupeng, Mei Fengxiang. GENERALIZED GRADIENT REPRESENTATION OF NONHOLONOMIC SYSTEM OF CHETAEV'S TYPE[J]. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(3): 684-691.

## GENERALIZED GRADIENT REPRESENTATION OF NONHOLONOMIC SYSTEM OF CHETAEV'S TYPE

• 摘要: 非定常非完整力学系统的稳定性研究是重要而又困难的问题,直接从微分方程出发来构造李雅普诺夫函数往往很难实现.本文给出了一种间接方法.提出了10类广义梯度系统的定义,并分别给出了10类广义梯度系统的微分方程.进一步研究一般切塔耶夫型非完整系统的广义梯度表示,给出该系统分别成为这10类广义梯度系统的条件,从而将切塔耶夫型非完整系统化成各类广义梯度系统.最后利用广义梯度系统的性质来研究切塔耶夫型非完整系统零解的稳定性.这种方法在直接构造李雅普诺夫函数发生困难时,显得更为有效.举例说明结果的应用.

Abstract: It is an important and di cult problem to study the stability of the non-steady and nonholonomic mechanical systems, and it is di cult to construct the Lyapunov function directly from the di erential equation. This paper gives an indirect method. The ten kinds of generalized gradient systems are proposed and the di erential equations of the ten kinds of generalized gradient systems are given respectively. Furthermore, the generalized gradient representations of a nonholonomic system of Chetaev's type are studied. The condition under which a nonholonomic system can be considered as a generalized gradient system is obtained, so the nonholonomic system of Chetaev's type is transformed into each generalized gradient systems. The characteristic of the generalized gradient systems can be used to study the stability of the nonholonomic system. This method appears to be more e ective when it is di cult to construct the Lyapunov function directly. Some examples are given to illustrate the application of the result.

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