Set the initial conditions of the system: initial angular speeds.

Um. The problem with that, is there are no "initial angular speeds". That is to say, there is simply no provision in the FEA software for the incorporation of 'speed' or 'momentum'.

Nor is there any need for it (in the FEA software). The (static) forces involved at any given position in space are the same regardless of how quickly you arrive at that point, or leave it. Indeed, if you think of something like a linear positioning motor on a CNC machine, most of the time the forces involved are those required to hold the workpiece (or tool) stationary against the cutting forces. And the magnetic forces are the same at startup, as they are for any given instantaneous position during traversal.

Now, whether I could (or should) attempt to perform the calculus required, to discretise the continuous motion between snapshots taken from the FEA, is really a moot point. To do it with any real accuracy, would -- I think -- require breaking the motion between FEA steps into 10s or preferably 100s of smaller steps. In addition to being a complexity I would rather not deal with, it would take considerable time.

Also, magnetism is often non-linear. For example, if materials move into magnetic saturation, the effects are distinctly non-linear. And at (and around) points of equilibrium, magnetic affects are subject to perturbations, which cause unpredictable instabilities (see Earnshaw's Theorum). Whilst the FEA takes all that into consideration on an instantaneous (static) basis; attempting to interpolate between static points in a linear fashion would inevitably result in non-linear jumps between frames. Better to use smaller steps and more FEA analysies than to try and second guess it, by re-writing it externally, I think.

As is, with the FEA taking an hour or more to integrate the forces for any given run, and my desire to run the model through at least one FEA analysis for each degree of rotation around B; the time-cost of the processing is already many days. I am reluctant to add substantially to that; especially as the result of the process is the production of a visualisation -- a movie -- from which no quantitative information can usefully be derived. And further because the desire is to produce a new movie after any (major) changes to the physical design of the apparatus.

The desire for the visualisation is to allow subjective, qualitative, side-by-side comparisons of the design iterations; to pick out break-point boundaries; maxima and minima; and similar events as the design progresses; to literally be able to 'see' the effects that changes have. Thus, the quantitative accuracy of the position in any given frame of the movie is of far less importance than that those frames consistently reflect the tried & tested (nearly 20 years to date) outputs of the FEA software.