Abstract. For the ball gyroscope it is shown that the interaction of the unbalanced rotor and the first harmonic component of the perturbing motor torque is the cause of care, which depends on the phase angle of the rotating magnetic field of the electric motor. The frequency of perturbation is a multiple of the rotor rotation frequency. The influence of synchronous and asynchronous components of the electromagnetic forces momentum on the gyroscope dynamics is also considered. It is evident from the expressions of the escapes that the mean phase angle θ of the rotating stator magnetic field can turn to zero, which coincides with the recommendations proposed by the previous authors. Quantitative estimates of the errors of the ball gyroscope are given.

Key words: perturbation torque of electric motor, imperfections of synchronous electric motor, amplitudes of angular variables, “polar” perturbation torque of synchronous hysteresis gyro motor, care of gyroscope with spherical support.