论文标题
消除亚伯拉罕·洛伦兹运动方程的病理解决方案
Elimination of Pathological Solutions of the Abraham-Lorentz Equation of Motion
论文作者
论文摘要
一个多世纪以来，亚伯拉罕 - 洛伦兹方程通常被认为是对带电粒子的动力学的正确描述。然而，亚伯拉罕 - 洛林兹方程的病理解决方案，其中粒子在施加力之前加速了，所谓的预循环溶液以及粒子在没有外部力的情况下即使在外部力的情况下也会自发加速的溶液，也被称为失控的解决方案。 Runaways违反了能源的保护，而预审经违反了因果关系。在这项工作中，我将重点关注最常用的运动方程之一：没有病理解决方案的Landau-Lifshitz方程。但是，这是亚伯拉罕 - 洛伦兹方程的一阶近似，提出了一个问题，即近似值如何比原始的问题更好。最后，提出了各种外力的一些数值结果，以比较两个方程。
For more than a century the Abraham-Lorentz equation has generally been regarded as the correct description of the dynamics of a charged particle. However, there are pathological solutions of the Abraham-Lorentz equation in which a particle accelerates in advance of the application of a force, the so-called preacceleration solutions, and solutions in which the particle spontaneously accelerates even in the absence of an external force, also known as runaway solutions. Runaways violate conservation of energy while preacceleration violates causality. In this work, I will focus on one of the most used alternative equations of motion: the Landau-Lifshitz equation, which has no pathological solution. However, it is a first-order approximation to the Abraham-Lorentz equation, raising the question of how an approximation turns out to be better than the original. Finally, some numerical results for a variety of external forces are presented to compare both the equations.
