Abstract
The purpose of this study is to investigate the effect of attachment errors of two beam-type flexible appendages mounted on a rigid body along the spin axis. For such a system, the sufficient conditions for achieving asymptotical dynamic stability are maximization of the moment of inertia about the spin axis and existence of a lower limit of the beam's natural frequency against the spin rate; these conditions can be acquired by Lyapunov's direct method. However, such conditions are limited to ideal configurations; for realistic satellites, attachment errors are unavoidable. In this study, each appendage that simulates a continuously flexible beam is modeled as a mass particle connected to the rigid body's space through springs. This paper illustrates mathematical formulations for acquiring the equilibrium state and determining the dynamic stability using Lyapunov's direct method. Numerical examples show that attachment errors either improve or worsen the stability in terms of the sufficient conditions.
