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The major objectives of the paper are to clarify the influence of a whirling motion on the electrical characteristics of a rotating electric machine and to propose a method to control the whirling motion under mechanical resonance. First, it is shown that the hysteretic jump phenomena exist in the rotating speed and the power consumption of the motor due to the whirling motion around the natural frequency. The jump of the rotating speed means that a continuous change of output power in a generator can not be achieved under mechanical resonance. The jump of the power consumption gives a large fluctuation to other rotating electric machines connected to the same power source. Second, we propose a torque-based control method that can suppress the whirling motion by controlling a torque. The control input is determined based on a stability condition for a time-varying system that is represented by a second-order vector differential equation with time-varying coefficient matrices. Stability of the system can be checked by the qualitative characteristics of its coefficient matrices. Finally, the effectiveness of our control method is discussed by both a simulation and an experiment.