In this paper we study the non-relativistic dynamic of a charged particle in the electromagnetic field induced by a periodically time dependent current $J$ along an infinitely long and infinitely thin straight wire. The motions are described by the Lorentz–Newton equation, in which the electromagnetic field is obtained by solving the Maxwell’s equations with the current distribution $\overrightarrow{J}$ as data. We prove that many features of the integrable time independent case are preserved. More precisely, introducing cylindrical coordinates, we prove the existence of (non-resonant) radially periodic motions that are also of twist type. In particular, these solutions are Lyapunov stable and accumulated by subharmonic and quasiperiodic motions.

在本文中，我们研究了周期相关电流在电磁场中带电粒子的非相对论动力学 $Ĵ$沿着无限长且无限细的直线。用洛伦兹-牛顿方程描述运动，其中电磁场是通过用电流分布求解麦克斯韦方程来获得的$\overrightarrow{Ĵ}$作为数据。我们证明了可积分时间无关情况的许多特征得以保留。更准确地说，通过引入圆柱坐标，我们证明了（非共振）径向周期性运动的存在，该运动也是扭曲类型的。这些解决方案尤其是Lyapunov稳定的，并通过次谐波和准周期运动积累。