On Lagrangian Theory for Rotating Charge Coupled to the Maxwell Field
Valeriy Imaykin, Alexander Komech, and Herbert Spohn
TL;DR
This paper rigorously justifies the Hamilton least action principle for the Maxwell-Lorentz equations involving Abraham's rotating extended electron, using variational Poincare equations on SO(3) to derive conservation laws.
Contribution
It introduces a novel application of variational Poincare equations on SO(3) to derive conservation laws in the Maxwell-Lorentz system with a rotating electron.
Findings
Established the Hamilton least action principle for the system.
Derived conservation laws using Noether's theorem.
Applied variational Poincare equations on SO(3).
Abstract
We justify the Hamilton least action principle for the Maxwell-Lorentz equations with Abraham's rotating extended electron. The main novelty in the proof is application of the variational Poincare equations on the Lie group SO(3). The variational equations allow to derive the corresponding conservation laws from general Noether theory of invariants.
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Taxonomy
TopicsNonlinear Waves and Solitons · Black Holes and Theoretical Physics · Gas Dynamics and Kinetic Theory