  We theoretically investigate the properties of magnetically-levitated
superconducting rotors confined in anti-Helmholtz traps, for application in
magnetomechanical experiments. We study both the translational modes and a
librational mode. The librational mode gives an additional degree of freedom
that levitated spheres do not have access to. We compare rotors of different
shapes: ellipsoids, cylinders and cuboids. We find that the stable orientations
of the rotors depend on the rotors' aspect ratios.
