Bifurcations and chaotic motions in a rate gyro with a sinusoidal velocity about the spin axis

Abstract

An analysis is presented for a single-axis rate gyro mounted on a space vehicle undergoing sinusoidal motion and steady rotation about its spin and output axes. By varying the amplitude of sinusoidal motion, the periodic and chaotic responses of this parametrically excited non-linear system are investigated using the incremental harmonic balance (IHB) method and numerical integration. The multi-variable Floquet theory is applied to analyze the stability of periodic attractors and the behavior of bifurcations. Additionally, phase portraits, Poincare maps, average power spectra, bifurcation diagrams, parametric diagrams and Lyapunov exponents are presented to observe Hopf bifurcation, symmetry-breaking bifurcations, period-doubling bifurcations and chaotic motions. The cell mapping technique (MICM) is also used to study the basins of attraction of periodic attractors. (C) 1997 Academic Press Limited