Quaternion Mathematics in Electromagnetic Modeling and Simulation

TL;DR

This paper explores the application of quaternion mathematics to improve electromagnetic field modeling, addressing vector representation issues in Maxwell's equations, and demonstrates its effectiveness through various dynamic scenarios.

Contribution

It introduces a quaternion-based rotation matrix for electromagnetic modeling, offering a novel approach to handle polar and axial vector distinctions in electromagnetic fields.

Findings

Quaternion approach accurately models magnetic fields from moving charges.

Differences in magnetic field observations are evident with moving observers.

Quaternion methods outperform traditional Maxwell's equations in dynamic scenarios.

Abstract

The purpose of this effort is to investigate if the use of quaternion mathematics can be used to better model and simulate the electromagnetic fields that occur from moving electromagnetic charges. One observed deficiency with the commonly used Maxwell's equations is the issue of polar versus axial vectors; the electromagnetic field E is a polar vector, whereas the magnetic field B is an axial vector, where the direction of rotation remains the same even after the axial vector is inverted. This effort first derived the rotation matrix for quaternion geometry. This rotation matrix was then applied to modeling the magnetic fields at a distance from a source, and comparing it to traditional Maxwell's equations. This effort was taken to model a series of moving charges, an observation aircraft observing a submarine, as well as an eddy current dynamic brake. It was clearly observed that when a moving observer is studying a moving target, differences in the magnetic direction and magnitude can be observed, demonstrating the effectiveness of quaternion mathematics in such applications.