This work applies the contact formalism of classical mechanics and classical field theory, introduced by Herglotz and later developed in the context of contact geometry, to describe electromagnetic systems with dissipation. In particular, we study an electron in a non-perfect conductor and a variation of the cyclotron radiation. In order to apply the contact formalism to a system governed by the Lorentz force, it is necessary to generalize the classical electromagnetic gauge and add a new term in the Lagrangian. We also apply the k-contact theory for classical fields to model the behavior of electromagnetic fields themselves under external damping. In particular, we show how the theory describes the evolution of electromagnetic fields in media under some circumstances. The corresponding Poynting theorem is derived. We discuss its applicability to the Lorentz dipole model and to a highly resistive dielectric.

这项工作应用经典力学的接触形式和经典场论，由 Herglotz 引入，后来在接触几何的背景下发展起来，来描述具有耗散的电磁系统。特别是，我们研究了非完美导体中的电子和回旋辐射的变化。为了将接触形式应用于由洛伦兹力控制的系统，有必要推广经典的电磁规范并在拉格朗日中添加一个新术语。我们还将经典场的 k 接触理论应用于模拟电磁场本身在外部阻尼下的行为。特别是，我们展示了该理论如何描述在某些情况下媒体中电磁场的演变。推导出相应的坡印廷定理。