平面上两电荷在磁场中的特殊运动轨迹
Two charges on plane in a magnetic field: special trajectories
摘要：
本文研究了在垂直于平面的恒定磁场作用下，平面$(e_1, m_1)$和$(e_2, m_2)$上两个库仑荷的经典力学。特殊的“超可积”的轨迹（圆形和线性），其中电荷之间的距离保持不变，以及他们尊重的运动常数。特殊轨迹的独立运动常数的数目比一般轨迹的大。对出现特殊轨迹的电荷对进行了分类。明确地描述了两个电子（电子-正电子）、（电子- $α$ -粒子）三种特殊情况下的特殊轨道.
英文摘要：
A classical mechanics of two Coulomb charges on a plane $(e_1, m_1)$ and $(e_2, m_2)$ subject to a constant magnetic field perpendicular to a plane is considered. Special "superintegrable" trajectories (circular and linear) for which the distance between charges remains unchanged are indicated as well as their respectful constants of motion. The number of the independent constants of motion for special trajectories is larger for generic ones. A classification of pairs of charges for which special trajectories occur is given. The special trajectories for three particular cases of two electrons, (electron - positron), (electron - $α$-particle) are described explicitly.
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