Appell方程的广义梯度表示及其稳定性分析  

Generalized Gradient Representations of Appell Equations and Its Stability Analysis

作　　者：崔金超[1] 廖翠萃 王勇[2] CUI Jin-chao LIAO Cui-cui WANG Yong(School of Science, Jiangnan University, Wuxi ,Jiangsu 214122, China School of Information Engineering, Guangdong Medical College, Dongguan,Guangdong 523808, China)

机构地区：[1]江南大学理学院,江苏无锡214122 [2]广东医学院信息工程学院,广东东莞523808

出　　处：《北京理工大学学报》2017年第2期216-220,共5页Transactions of Beijing Institute of Technology

基　　金：国家自然科学基金资助项目(11272050;11401259);江南大学自主科研计划资助项目(JUSRP11530);广东医学院科研基金面上资助项目(M2011043)

摘　　要：Appell方程是分析力学中的一类重要方程,该方程既可以用来描述完整系统又可以用来描述非完整系统.通过将Appell方程表示为广义梯度形式,进而可以借助梯度系统的某些性质来研究Appell方程的解及其稳定性问题.为此,本文先将梯度系统推广为包含时间变量的广义梯度系统,再给出Appell方程可化为广义梯度系统的条件,最后利用广义梯度系统的性质来研究Appell方程解的稳定性问题,并结合实际例子说明理论的应用.Appell equation is a kind of important equations in analytic mechanics,which is not only suitable for holonomic systems but also applicable to nonholonomic systems.In order to study the stability of solutions of Appell equations,the gradient systems were extended to generalize gradient systems which contain the variable of time.Two kinds of generalized gradient systems were put forward and the characteristics of the systems were studied.The conditions under which Appell equations could be considered as one of two generalized gradient systems were obtained.Then,the stability of solutions of Appell equations were studied based on the characteristics of generalized gradient systems.Some application results show the feasibility.

关 键 词：分析力学 APPELL方程 广义梯度系统 解的稳定性分析 

分 类 号：O316[理学—一般力学与力学基础]