Nielsen方程的广义梯度表示及其稳定性分析  

Generalized Gradient Representation of Nielsen Equation and Its Stability Analysis

作　　者：尹明旭 谢煜 陈向炜 YIN Mingxu;XIE Yu;CHEN Xiangwei(Collge of Mathematical Sciences,Suzhou University of Science and Technology,Suzhou 215009,Jiangsu,China;Collge of Electronic and Electrical Engineering,Shangqiu Normal University,Shangqiu 476000,Henan,China)

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

出　　处：《力学季刊》2022年第2期340-354,共15页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金(11372169)。

摘　　要：研究Nielsen方程的广义梯度表示以及方程零解稳定性.首先给出4类广义梯度系统及其性质.其次,给出完整系统和非完整系统的Nielsen方程转化成广义梯度系统的条件;将两类Nielsen方程分别化为广义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并通过数值模拟验证结论的准确性.This paper investigates the generalized gradient representation of the Nielsen equations and the stability of the zero solution of the equations.Firstly,four types of generalized gradient systems and their properties are given.Secondly,the conditions for transforming the Nielsen equation of the complete or non-holonomic system into the generalized gradient systems are given.The two types of Nielsen equations are respectively transformed into the generalized gradient systems,and the stability of the zero solution of the equations is studied.Finally,examples are given to verify the applicability of the results,and the accuracy of the conclusions is validated through numerical simulations.

关 键 词：NIELSEN方程 广义梯度系统 稳定性 数值模拟 

分 类 号：O316[理学—一般力学与力学基础]