This paper concerns the response of a gyropendulum subject to vertical harmonic excitation. Instability of the Mathieu type is shown to occur, the principal region of instability lying about the nutational frequency of the system. Experimental results are presented which clearly indicate the validity of the theoretical prediction. It is also shown that an unstable gyroscopic system can be stabilized by vibrating the equipment with the proper choice of vibration parameters. In such cases, the additional stabilizing factor has been analytically derived. Based on the above analysis, practical suggestions for instrument design are also provided.
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References
1.
KrishnanV.Dynamics of a gyropendulum for small angles. J. Mech. Engng. Sci., 1980, 22(5), 265–266.
2.
MathewsR. J.Combination gyro and pendulum weight passive antenna stabilized platform system. US Patent No. 4020491, Jan. 1979.
3.
ArnoldR. N.MaunderL.Gyrodynamics and its engineering applications, 1961, Academic Press.
4.
McLachlanN. W.Theory and application of Mathieu function, Dover Publication Inc., New York, 1964.
5.
KabakowH.A perturbation procedure for weakly coupled oscillations. Int. J. Nonlinear Mechanics, 1972, 7, 125–137.
6.
FedorchenkoA. M.On a dynamic method of increasing the stability of a rapidly rotating symmetrical gyroscope. J. App. Math. Mech., 1961, 25(5), 1406–1410.
7.
BogolinbovN. N.MitropolskyY. A.Asymptotic methods in the theory of nonlmear oscillations, Hindustan Publishing Company, India, 1961.
8.
KrishnanV.Dynamics of gyroscopes controlled by gravity. PhD thesis, University of Newcastle upon Tyne, July 1978.
