The Modeling of Electricity and Magnetism

Once you are taught an assured way of how Nature is represented, alternative approaches tend to be ignored. Here I will discuss a concept described in the 19th Century, driven into obscurity in the 20th only to be rediscovered in the computing age. The story contains a mathematical discussion of the phenomena of electricity and magnetism, one of the four fundamental forces of physics, in terms of planetary constraints. This story is intertwined between the following literature:

Maxwell's Theory The one appearing in the Third Edition, 1904.

Hamilton's Quaternions A brilliant work that reads eerily modern. Nevertheless, it helps if you know what you should only pay attention to the rotational character of the algebra and use the term "versor" as opposed to the more familiar "vector" since Hamilton himself caused great confusion when he tried to do both at the same time to describe coordinate transformations.

My contribution Having studied a portion of Maxwell's original equations from A Dynamical Theory of the Electromagnetic Field (1865) from the perspective of polar coordinates in terms of a MoM, FEM-based model and solution in my dissertation and publications, I will apply what I learned, what I did wrong, and what I think I did right to what I believe is a complete interpretation of the stored energy and motional dynamics including magnetic field geometry and forces in a wireless-powered circuit, the Model 'G7' oscillator. The mathematical model will employ quaternions to map composed field dynamics to simulation and physical prototype.