Talk:Spin-stabilized magnetic levitation
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Earnshaw's Theorem
Your explanation of the Levitron only deals with the mechansim which prevents the levitating magnet from turning over or slipping sideways.
It does not address the issue of the existence of a stability node in the vertical plane.
If we are going to discuss Earnshaw's Theorem, then this question needs to be addressed whether in the case of the Levitron, or in the case of levitating ring magnets placed over a pole, or in the case of levitating bar magnets in a test tube, or in the case of trains that are magnetically levitating above the railway track.
In fact you are quite wrong when you state in the main article that Earnshaw's Theorem doesn't apply just because the magnet is spinning. You have completely misunderstood what Earnshaw's Theorem means.
Although Earnshaw's Theorem comes directly from Gauss's Law and refers to equilibrium nodes between static objects, the term static in this context means the absence of linear motion. Gauss's Law tells us that there can be no equilibrium nodes between static objects if the only forces involved obey the inverse square law.
It is a totally specious argument to claim that Gauss's Law ceases to apply simply because the Levitron is spinning and is therefore not technically static. The Levitron is static for the purposes of Gauss's law and to say otherwise is merely a specious play on words. The spin of the Levitron cannot possibly introduce an up/down stability node as between the magnetic force and the gravitational force. That stability node is there anyway, as can be demonstrated by levitating static ring magnets over a pole. And it is the existence of that stability node which is the subject of controversy. The Levitron's spin has got absolutely nothing to do with the controversy over Earnshaw's Theorem. (61.7.159.2 07:07, 17 April 2007 (UTC))
There are two ways out of the dilemma regarding the up/down stability node.
(1)The magnetic force upwards is not an inverse square law force.
(2)The magnetic force of repulsion does obey the inverse square law but its numerator is less than the GM in the numerator of the gravitational force downwards. (GM refers to the Universal gravitational constant multiplied by the mass of the Earth)
Since the origin for the gravitational force's coordinate system is at the centre of the Earth, whereas the origin for the magnetic force's coordinate system is at the base of the apparatus, then the two inverse square law graphs could indeed intersect each other and create a stability node.
If either of these are the case, then Earnshaw's Theorem is not breached but may have been mis-extrapolated from is 1839 origins to apply across systems using different coordinate frame origins.
It's quite possible that the controversy surrounding Earnshaw's Theorem and Magnetic Levitation has all been a storm in a tea cup. Magnetic Levitation does occur. One thing is sure and that is that this issue has not been dealt with in the main article. The main article discusses gyroscopic reasons that prevent side slipping and turning over. (61.7.150.204 11:52, 17 April 2007 (UTC))