【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.更多还原

【Abstract】 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.更多还原