Original poster: Steve Conner <steve@xxxxxxxxxxxx>
One could most likely adapt an already worked solution borrowed from mechanics to nail down the equations of "frequency splitting"
Or you could just look them up on Richie Burnett's website.Seriously, frequency splitting is perfectly well understood. It follows naturally from the differential equations that describe the electrical behaviour of the Tesla coil system.
It happens that I do have a background in mechanical engineering, and I do like to think about it in terms of the problems we were taught in dynamics that use a load of matrix equations to find the resonant frequencies of a structure. The maths is pretty much identical.
Steve Conner