The commercial toy, Levitron, can achieve stable magnetic levitation

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The commercial toy, Levitron, can achieve stable magnetic levitation due to gyroscopic stabilization and axis precesion. The Levitron toy sold in market has a vertical spinning axis, and so far I have not found a variation with horizontal axis.

Is it allowed in Earnshaw's theorem, for a magnetic system to have stable levitation, just by rotation alone, in a horizontal spinning axis?

Thanks in advanced.
 
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Not familiar with Earnshaw's Theorem (will look it up later), but a horizontally rotating levitron would have its positive and negative polls alternately pointing toward the magnet beneath. This would not levitate, asthe equall times of being attracted and repelled by the base would cancel out, and gravity would assert itself.
 


True, the magnetic configuration of Levitron doesn't allow it to rotate on horizontal axis. I did try other magnetic configuration but it doesn't work out as well.

However, can we generalize, that for ANY magnetic configuration, the system wouldn't be able to levitate stably and rotating on horizontal axis?
 


I believe it is a fair generalization. The nature of magnetic levitation requires a vertical force that holds constant. That would seem to dictate the need for both the base and the levitating object to remain vertically stable. I, at least, can think of no way around that (although my imagination is admittedly quite limited).
 


OK, a few minutes of thinking did yield a tantalizing possibility. If both the levitator and the base were revoling at the same rate, so that like poles always faced one another, that might work. Ity would be a nightmare to try to impliment, though.