Abstract
The motion of a rigid body about fixed point with small radial mass-unbalance in homogeneous gravitational field was discussed. The dynamical equations described by state variables of the body were established, and approximate analytical solutions for a spinning body with high speed were obtained by use of the average method. The influence of the radial mass-unbalance of the rotor to the precession character of a free-rotor gyroscope was analyzed. And a physical explanation of the drift phenomenon of the gyro was given. An applicable formula of gyro's constant drift in analytical form was obtained, which is perfectly coincident with the numerical calculation.
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