Here's a confession: our ultimate research goal is to complete Weber's proposal on the molecular structure of atoms according to his proposed electrodynamics.
This would mean classifying the semistable states of various $N$-body electrical systems. This was outlined by Wilhelm Weber in one of his final posthumously published memoirs. Insert reference.
We can numerically simulate these solutions using odeint on python. We fix the centre of mass of the system as the origin reference point, and can integrate the equations of motion using Weber's force law. This is complicated $N$-body system, so what can we reasonably expect to prove ?
When we write $-2=-1-1$ we mean considering $-2$ as a two-body system which is stable, i.e. two identicaly negative charges have been forced through the critical radius and stably attracted to each other.
- We should classify the $(-2) + (+1)$ system, which consists of three particles. In other words, does the system collapse? Or is it a stable planetary type system, i.e. the two-body system $(-2)$ rotates with precession about the $(+1)$ charge. This would require a simulation.
Classifying the stable orbits of the above three-body system, which has net charge $-1$ (!) would be very interesting starting point. In Ralph Sansbury's model, the above system represents the electron, and in this sense Sansbury speaks of the structured electron. The question which needs be considered is what is the internal potential energy of the above system, i.e. at what energies can it be separated ? Because we do not typically see the electron disintegrating into smaller subsystems. But it's possible that the system has an extremely large cohesion energy, and that if the system ever degenerated, then particles travelling at velocities greater than $c$ would be observed. And this possibility is not ruled out a priori by the Weber electrodynamics.
There is an obvious multiplicity in the possible configurations once you allow the possibility of the electron as being structured of smaller systems. And this is where we need simulation, because I'm not sure we can work out the theory a priori. That is, the energy landscape of the Weber potential is not well known for many-body systems, and simulation is a good way to start learning.
For example the four-body systems with zero net charge could have various configurations. Likewise the six body systems with zero net charge, etc..
Here we implicitly assume a zero net charge to represent the stable molecular atoms. This implies an even number of particles. However we do not require the inertial masses $m_+$ and $m_-$ to be equal a priori. And in practice we find the proton significantly heavier than the conventional electron. In light of Sansbury's proposal, we need a heuristic to find the order of magnitude of the indivisible negative charges $(-1)$ and positive charges $(+1)$.
There is very interesting idea of Ralph Sansbury which calls "metastable orbits". This is Sansbury's explanation for the apparent nonradiation of the hydrogen atom. In fact, there is radiation between the subsystems, but there is zero net radiation into the environment! That's Sansbury's brilliant idea. (He has others.)
