I'm making a toy, partly to use a couple of ferrite ring magnets that I've liberated from a magnetron, and partly to see whether I'm capable of stabilising the control loops that will be required.
The idea is to use one magnet vertically above the other, oriented so they repel. This equilibrium is stable in height y, but is unstable in the x and z position, and also in the tilt of the floating magnet. I plan to sense the position and tilt of the magnet with capacitive sensing, and control them with air-core electromagnets.
Here's a very abbreviated sketch of the system, showing only the x axis control coils, cyan in the yz plane for torquing the magnet about the z axis, dark blue in the xz plane for displacing it along the x axis. There will be another set along the z axis. Not shown are the position sensors or the caging/support arrangement.
The symmetry of the picture invited the thought of what happens if the top magnet is spun, perhaps by a tangential jet of air. At rest, z axis torque will turn the magnet about the z axis. However at a high enough angular speed, gyroscopic action will mean that the magnet precesses about x rather than z. This would then require each tilt loop to control the other axis.
Finally the question(s).
What happens at low spin speed?
Do I need to switch from static behaviour to gyroscope behaviour at some critical spin speed?
Or is the behaviour always mixed, with the quadrature torque needed proportional to the spin speed? (which ratio between static and gyroscopic gives me the 'critical' speed?)
I've gone cross-eyed trying to do the thought experiment, and the physical one is quite a while off yet.