Double degeneracy and chaos in a rate gyro with feedback control

Abstract

The analysis of a single-axis rate gyro subjected to feedback control mounted on a space vehicle that is spinning with uncertain angular velocity omega(2) about its spin of the gyro is presented. For the autonomous case in which omega(2) is steady, we examine the dynamics of the resulting system on the center manifold near the double-zero degenerate point by using center manifold and normal form methods. There exist a few kinds of bifurcations in the autonomous case such as pitchfork and Hopf bifurcations for local bifurcation analyses, and a saddle-connection bifurcation for global analyses. As singular velocity omega(2) of the space vehicle is harmonic, the Melnikov technique was used to give criteria for the existence of chaos in the gyro motion. The numerical simulations are performed to verify the analytical results in the form of phase portraits, bifurcation diagrams and Lyapunov exponents. In addition, chaotic motions of this system can be changed into regular motions by a small parametric perturbation with Lyapunov exponent calculations. (C) 1998 Academic Press Limited.