Double Ring Question

[Kirill Danilov]

For a dumbell suspended between two rings, the configurations are given by the sign of alpha, a factor that is wholly dependent on the difference between the double of the square of the radius of the rings and the square of their distance from each other. For alpha positive, it is a ring radius sufficiently smaller than this height, and in such a case the energy is lowest for a horizontally placed dumbell. For alpha positive, it is a ring radius greater than this height and the lowest energy is a vertically placed dumbell. For alpha zero, this is a point when the quadrupole energy has no contribution for this term and the orientation of the dumbell does not change the energy.

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