An analysis is presented in this paper for a two-axis rate gyro subjected to linear feedback control mounted on a space vehicle, which is spinning with uncertain angular velocity ωZ(t) about its spin of the gyro. For the autonomous case in which ωZ(t) is steady, the stability analysis of the system is studied by Routh-Hurwitz theory. For the non-autonomous case in which ωZ(t) is sinusoidal function, this system is a strongly non-linear damped system subjected to parametric excitation. By varying the amplitude of sinusoidal motion, periodic and chaotic responses of this parametrically excited non-linear system are investigated using the numerical simulation. Some observations on symmetry-breaking bifurcations, period-doubling bifurcations, and chaotic behavior of the system are investigated by various numerical techniques such as phase portraits, Poincaré maps, average power spectra, and Lyapunov exponents. In addition, some discussions about chaotic motions of this system can be suppressed and changed into regular motions by a suitable constant motor torque are included.
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