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For large flywheel rotors supported by high-temperature superconducting (HTS) bearings, the amplitude of sub-synchronous whirl can become so large that it limits the maximum speed to a value less than that dictated by its mechanical strength. Internal damping, in the form of hysteretic loss in the rotor material, creates a force that adds energy to the forward whirl. We examine the effect of internal damping as the cause of the sub-synchronous whirl and show that theoretical predictions of the onset criteria agree with experimental data. We next show how it is possible to damp the whirl from a theoretical context and discuss a practical approach to accomplish this that has had success in our laboratory experiments.