Dynamics and control properties for an asymmetric dumbbell spacecraft

Relative equilibria of a dumbbell-type spacecraft consisting of two bodies separated by an elastic link is studied in a central gravitational field. The only other forces present in the system are two internal forces acting on the spacecraft to control its attitude and its shape. Linearized equations from the Routh reduction technique are derived. These are used to demonstrate the local controllability properties for the attitude, shape, and orbital equations of the dumbbell spacecraft. Stability conditions of the relative equilibria are determined and then analyzed through examples. The effects of the gravity gradient, and the coupling between attitude, shape, and orbital dynamics, can be used to change the energy of the spacecraft. Thus, through control of the attitude and/or shape, the orbit of the spacecraft can be modified with minimal fuel expenditure