Analysis and simulation of a controlled rigid spacecraft: stability and instability near attractors

The authors give an analysis and simulation of the asymptotic properties of various closed-loop trajectories of the rigid-body model of a controlled spacecraft. Recent results are described which show that the rigid body for a spacecraft controlled by two independent pairs of gas jets is locally controllable but not locally asymptotically stabilizable about reference attitudes. The authors analyze, in the context of feedback stabilization about an attractor, the asymptotic properties of closed-loop trajectories when a feedback law driving the motion to a revolute cycle about a principle axis is implemented. Simulations support such convergence but indicate that convergence is quite slow, due to the fact that this cycle lies, as it must, on an invariant center manifold for this system. In particular, while the design is based on a nonlinear enhancement of root-locus theory, such attractors have no linear analogue