I have recently come across Earnshaw's theorem in my research which states that it is not possible to stabilize an object using only static permanent magnets. I understand that and it makes sense to me.
My question is, is it possible to achieve stability with only one electromagnet and the help of gravity? The setup is illustrated below (sorry for the crude diagram):
(please imagine a heavy spinning load attached to the middle of the shaft between both sets of magnets)
The ferromagnetic shaft is pinned against the bottom passive magnet against gravity. The electromagnet at the top is controlled by a PID controller that measures the distance of the shaft from the electromagnet, and attempts to keep it at a constant distance.
The central magnets fix two rotational degrees of freedom and two translational degrees of freedom, the electromagnet fixes the last translational degree of freedom. The remaining DOF is the desired spinning motion.
Is this configuration stable, or are there any unstable paths the shaft can take that would lead to it eventually touching a magnet? Perhaps an unforeseen oscillatory motion of some kind? (since the shaft is fully encased in magnets and rapidly spinning, any failure mode is catastrophic)