Application of Herglotz's Variational Principle to Electromagnetic Systems with Dissipation

Abstract

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 term in the Lagrangian. We also apply the k-contact theory for classical fields to model the behaviour 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.

References in corpus (3)

• Extended Hamilton-Jacobi theory, contact manifolds and integrability by quadratures
• Generalized nonconservative gravitational field equations from Herglotz action principle
• Optimal control, contact dynamics and Herglotz variational problem

Cited by in corpus (6)

• Multicontact formulation for non-conservative field theories
• Symmetries, conservation and dissipation in time-dependent contact systems
• A variational derivation of the field equations of an action-dependent Einstein-Hilbert Lagrangian
• Inverse problem and equivalent contact systems
• Practical Introduction to Action-Dependent Field Theories
• When action is not least for systems with action-dependent Lagrangians