Chaotic dynamics of a spacecraft with a nearly symmetric flexible appendage and energy dissipation via a nonlinear controller

In this work, we study the attitude dynamics of a single body spacecraft that is perturbed by the motion of a small flexible appendage that is constrained to undergo only torsional vibration. In particular, we are interested in the chaotic dynamics that can occur for certain sets of the physical parameter values of the spacecraft when energy dissipation acts to drive the body from minor to major axis spin. Energy dissipation, which is present in all spacecraft systems and is the mechanism which drives the minor to major axis transition, is implemented via a quantitative energy sink that is modeled using a nonlinear controller. We obtain an analytical test for chaos in terms of satellite parameters and present numerical simulations which support and extend the analytical results.