## Drift motion of free-rotor gyroscope with radial mass-unbalance.(English)Zbl 1075.70006

Summary: We discuss the motion of a rigid body about fixed point with small radial mass-unbalance in homogeneous gravitational field. 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 average method. The influence of the radial mass-unbalance of the rotor on the precession character of a free-rotor gyroscope was analyzed. A physical explanation of the drift phenomenon of the gyro was given, and an applicable formula for gyro’s constant drift was obtained in analytical form, which is coincident with the numerical calculation.

### MSC:

 7e+06 Motion of the gyroscope 7e+18 Motion of a rigid body with a fixed point

### Keywords:

average method; constant drift
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### References:

 [1] Yan-zhu, Liu, Gyrodynamics[M] (1986), Beijing: Science Press, Beijing [2] Lange, B., Active damping of ESG rotors with mass-unbalance readout[J], Spacecraft & Rokets, 9, 2, 96-102 (1972) [3] Leimanis, E., The General Problem of the Motion of Coupled Rigid Bodies About a Fixed Point [M] (1965), New York: Springer-Verlag, New York · Zbl 0128.41606 [4] Yan-zhu, Liu, Quasi-Euler-Poinsot motion of a rigid body[J], Acta Mechanica Solida Sinica, 9, 4, 294-302 (1988) [5] Yan-zhu, Liu, The development of the dynamics of rigid body with state variables[J], Acta Mechanica Solida Sinica, 3, 3, 307-314 (1990) [6] Martynenko, Y. G., Motion of gyroscope with noncontact suspension and unbalance[J], Izv Akad Nauk SSSR, MTT, 14, 4, 13-19 (1974) [7] Beletsky, V. V., Motion of Satellite About Center of Mass[M] (1965), Moscow: Nauka, Moscow [8] Yan-zhu, Liu, The stability of the permanent rotation of a free multibody system[J], Acta Mechanica, 79, 1-2, 43-51 (1989) · Zbl 0687.70018 [9] Yan-zhu, Liu; Li-qun, Chen, Nonlinear Vibration[M] (2001), Beijing: High Education Press, Beijing
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