Analytical criterion for chaotic dynamics in flexible satellites with nonlinear controller damping

In this work, we study the attitude dynamics of a single body spacecraft that is perturbed by the motion of a small flexible appendage 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 that drives the minor to major axis transition, is implemented by a quantitative energy sink that is modeled with a nonlinear controller. We obtain an analytical test for chaos in terms of satellite parameters by Melnikov's method. This analytical criterion provides a useful design tool to spacecraft engineers who are concerned with avoiding potentially problematic chaotic dynamics in their systems. In addition, we show that a spacecraft with a control system designed to provide energy dissipation can exhibit chaos because of the inherent flexibility of its components.