Nonlinear Dynamics and Control of a Dumbbell Spacecraft System

This paper deals with the dynamics and control of multi-body systems in which their linear, rotational, and elastic motions are coupled. We model a multi-body spacecraft system as two rigid bodies that are connected by a nonlinear, elastic spring. It is assumed that the system travels in a planar orbit around a planet with a uniform gravitational field. The methodology developed in this paper leads to a simple nonlinear control law that allows us to control the coupled orbital, attitude, and elastic dynamics, and precisely maintain a prescribed tumbling trajectory for the spacecraft system. We show that complex motions like the precision tumbling of elastically vibrating spacecraft in orbit can be accomplished with considerable ease and accuracy. The proposed methodology reveals a systematic technique for controlling complex nonlinear, multi-body systems.