ANALYTICAL CRITERION FOR CHAOTIC DYNAMICS IN FLEXIBLE SATELLITES WITHNONLINEAR CONTROLLER DAMPING

In this work, we study the attitude dynamics of a single body spacecra ft that is perturbed by the motion of a small flexible appendage const rained to undergo only torsional vibration. In particular, we are inte rested in the chaotic dynamics that can occur for certain sets of the physical parameter values of the spacecraft when energy dissipation ac ts 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 quanti tative energy sink that is modeled with a nonlinear controller. We obt ain an analytical test for chaos in terms of satellite parameters by M elnikov's method. This analytical criterion provides a useful design t ool to spacecraft engineers who are concerned with avoiding potentiall y problematic chaotic dynamics in their systems. In addition, we show that a spacecraft with a control system designed to provide energy dis sipation can exhibit chaos because of the inherent flexibility of its components.