摘要
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.
作者
章婷婷
张毅
张成璞
陈向炜
Zhang Tingting;Zhang Yi;Zhang Chengpu;Chen Xiangwei(College of Mathematics and Physics,Suzhou University of Science and Technology,Suzhou 215009,China;College of Civil Engineering,Suzhou University of Science and Technology,Suzhou 215011,China;Department of Electrical and Electronic Engineering,Shangqiu Normal University,Shangqiu 476000,China;Department of Physics and Information Engineering,Shangqiu Normal University,Shangqiu 476000,China)
出处
《动力学与控制学报》
2019年第4期306-312,共7页
Journal of Dynamics and Control
基金
国家自然科学基金资助项目(11372169,11272227,11572212)~~
关键词
非完整系统
三重组合梯度系统
稳定性
nonholonomic systems
triple combined gradient method
stability
