Lorentz-Dirac模型的梯度表示与稳定性研究  

Research on gradient representation and stability of Lorentz-Dirac model

作　　者：尹明旭 陈向炜 YIN Ming-xu;CHEN Xiang-wei(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：《云南大学学报（自然科学版）》2023年第3期621-627,共7页Journal of Yunnan University(Natural Sciences Edition)

基　　金：国家自然科学基金(11372169).

摘　　要：研究Lorentz-Dirac模型的梯度表示及其平衡点稳定性.首先给出Lorentz-Dirac模型的运动方程以及4种基本梯度系统和6种二重组合梯度的定义和微分方程;其次,验证约化Lorentz-Dirac模型转化成梯度系统、斜梯度系统和组合梯度系统的可行性并给出具体表示;最后,通过将方程化为组合梯度系统研究其稳定性,举例验证结果的应用.The gradient representation of the Lorentz-Dirac model and the stability of its equilibrium point are studied.Firstly,the equation of motion of the Lorentz-Dirac model and the definitions and differential equations of the 4 kinds of basic gradient systems and 6 kinds of dual combined gradients are given.Secondly,the feasibility of transforming the reduced Lorentz-Dirac model into a gradient system,an oblique gradient system,and a combined gradient system is verified,and its specific expression is given.Finally,the stability is studied by converting the Lorentz-Dirac equation into a combined gradient system,and an example is used to verify the application of the results.

关 键 词：Lorentz-Dirac方程 稳定性 梯度系统 

分 类 号：O316[理学—一般力学与力学基础]