We use the classical approximation to the dual QCD field equations to calculate the term in the heavy-quark potential that is proportional to angular momentum squared. This potential combined with the potentials obtained in our earlier work gives a result which is essentially the dual of the potential acting between a monopole-antimonopole pair carrying Dirac electric dipole moments and rotating in a relativistic superconductor. These potentials are used to fit the masses of the low-lying states of the ccBAR and bbBAR systems. The agreement, achieved with only four parameters, two of which are roughly determined in advance, is better than 1%. We also predict the masses of the lightest cbBAR states.