  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.
