Stability of Dual-spin Spacecraft via Maximal Lyapunov Exponent Based Approach
by
Samuel F. Asokanthan
The University of Queensland, Brisbane, AUSTRALIA
Coauthors: X. H. Wang

The attitude stability of dual-spin spacecraft with unsymmetrical bodies has been a primary focus of attention in recent years. Several studies have been performed on the stability behaviour of dual spin spacecraft taking into account the rotor and platform asymmetry as well as the energy dissipation in the dampers and the joints in their dynamic models. The method of analysis had been primarily based on either the Floquet theory or on the method of averaging. It was also customary to use numerical methods based on Floquet theory and Hsu's scheme, as well as perturbation methods based on the method of multiple time scales. In the present paper, a technique based on evaluation of top Lyapunov exponents is applied to study the attitude stability behaviour of an asymmetric dual-spin spacecraft system which incorporates a flexible joint. It is well known that Lyapunov exponents characterise the exponential rates of change of the response of dynamical systems. The system is stable (unstable) if the maximal Lyapunov exponent is negative (positive). Thus, the vanishing of the largest Lyapunov exponent implies a change in the stability property of the system. The present study makes use of an efficient numerical scheme to numerically evaluate the top Lyapunov exponent. This scheme, originally proposed for a single degree of freedom system, lends itself for use with mult-idegree of freedom systems.

The equations that governs the attitude motion of the spacecraft, when suitably linearised, represent the motion of a multi-degree-of-freedom, non stationary, gyroscopic system. Simplified analytical models that are formulated in Hamiltonian form are established for the purpose of stability analysis. A numerical scheme for calculating the maximal Lyapunov exponent is developed to examine the stability of solutions of the equations of motion. The stability conditions relating the rotor speed and stiffness/inertia inequality factor are established. Instabilities that correspond to sub- harmonic as well as combination resonances have been identified by studying the sign of the top Lyapunov exponent. Instability regions are presented graphically in the excitation frequency-excitation amplitude-top Lyapunov exponent space. Predicted instability conditions have been shown to agree with those obtained previously using approximate analytical methods.

Date received: April 20, 1998

Copyright © 1998 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caav-21.