Stability of Gyro with Harmonic Nonlinearity in Spinning Vehicle

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A stability analysis of a single-axis rate gyroscope mounted in a space vehicle which is spinning with uncertain angular velocity ¿z about the spin axis of the gyro is presented. The complete nonlinear equation of motion, which includes the fundamental and second harmonic nonlinear terms, arising due to ¿z, is considered. For time-varying ¿z(t), using the circle criterion, it is shown that the gimbal motion is globally asymptotically stable if the Nyquist plot of the linear transfer function of the gyro lies in the interior of a certain disk. For the case of uncertain constant ¿z, using the Lyapunov approach, conditions for global asymptotic stability (GAS) and asymptotic stability are derived. Stable regions in parameter space of the gyro and state space are obtained. Analytical relations for the selection of gyro parameters are derived.


Angular velocity; Asymptotic stability; Extraterrestrial measurements; Gyroscopes; Nonlinear equations; Space vehicles; Spinning; Stability analysis; State-space methods; Transfer functions


Aerospace Engineering | Astrodynamics | Controls and Control Theory | Electrical and Computer Engineering | Electrical and Electronics | Electronic Devices and Semiconductor Manufacturing | Multi-Vehicle Systems and Air Traffic Control | Navigation, Guidance, Control and Dynamics | Power and Energy | Signal Processing | Structures and Materials | Systems and Communications


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