Below is the comment I wrote on Reddit some times ago (https://www.reddit.com/r/physicsmemes/comments/w0njlh/gluons_in_action/) about one my experiment video titled "Gluons" in action which showing a realization of a magnetic bound state solution. It summarizes the effect and explains how it works:
This video shows a bound state between two dipole magnetic bodies as ordinary neodymium magnets.
As a background theory, two magnets or anything can not be contactless bound statically by force fields alone, say gravitational, electrostatic or magnetic or their any combinations as stated by the Earnshaw theorem. However this can be achived when inertial forces are involved. In this case, we have also inertial forces and torques, therefore requires acceleraration and motion.
This magnetic interaction might be compared to orbital mechanism in this basis. That is, classical mechanics. For example planets are bounded to the Sun by the balance of gravitational force of the sun and the inertial force receives planets through thieir curved trajectory, defined by Newton's second law (F = m a). Here, in this magnetodynamic interaction, there is a interplay between inertial force and magnetic force again, but rather in terms of torque and rotational (angular) motion. So the floating magnet does angular motion (but keeping its position almost constant) as one can see in this video. This motion resembles to one's body while playing hula-hoop. This motion has also a specific timing respect to the rotating field which is called "phase lag" inherited from harmonic motion where the direction of the force and the displacement are in opposite directions all the time. This translates to this: The pole S of the rotating magnet pulls the pole N of the floating magnet, but due to this opposition, this pole N instead gets closer to the rotating magnet pole N. So as same polarities repel each other, the net result is a repulsion. Here there is also a trick on the rotating magnet where poles are slightly off the rotation plane. This asymmetry causes a magnetic attraction. This magnetic attraction and the above mentioned repulsion can balance each other. This is a stable balance because repulsion varies twice as fast than the attraction by varying the distance. Here the gravity (weight of the floating magnet) tries to disturb the balance but I choose a configuration good enough to prevent it. That's all. See the linked article in the video description explaining this in 100 pages with equations, simulations, illustrations, pictures, various configurations and features.
