Nielsen方程的三重组合梯度表示及其稳定性分析  

The Triple Combination Gradient Representation Of Nielsen Equation and Its Stability Analysis

作　　者：尹明旭 陈向炜 Yin Mingxu;Chen Xiangwei(Collegr of Mathematical Sciences,Suzhou University of Science and Technology,Suzhou 215009,China;College of Electronic and Electrical Engineering,Shangqiu Normal University,Shangqiu 476000,China)

机构地区：[1]苏州科技大学数学科学学院,苏州215009 [2]商丘师范学院电子电气工程学院,商丘476000

出　　处：《动力学与控制学报》2023年第2期24-32,共9页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(11372169)。

摘　　要：研究Nielsen方程的三重组合梯度表示以及方程零解稳定性.首先给出4类三重组合梯度系统及其性质.其次,给出完整系统和非完整系统的Nielsen方程转化成三重组合梯度系统的条件;将完整和非完整两类Nielsen方程分别化为三重组合梯度系统并研究方程的零解稳定性.最后,举例验证结果的应用.The triple combination gradient representation of Nielsen equation and the stability of the zero solution of the equation are studied.First,four kinds of triple combination gradient systems and their properties are given.Secondly,the conditions for transforming Nielsen equations of complete and nonholonomic systems into triple combination gradient systems are given;The two types of Nielsen equations are respectively transformed into triple combined gradient systems and the stability of the zero solution of the equations is studied.Finally,examples are given to verify the application of the results.

关 键 词：NIELSEN方程 组合梯度系统 稳定性 

分 类 号：O316[理学—一般力学与力学基础]