An elastic dumbbell spacecraft is assumed to consist of two identical mass particles that are connected by a long elastic link. The motion of the dumbbell spacecraft can be described by orbit, attitude and shape dynamics that arise due to gravitational forces, an elastic restoring force along the longitudinal axis of the spacecraft, and control forces that act to change the attitude and shape of the spacecraft. These control forces have the property that there is no net external force on the dumbbell spacecraft. Since the angular momentum of the spacecraft is necessarily conserved, Routh reduced equations of motion are developed that describe the reduced dynamics of the controlled spacecraft. The reduced equations of motion are developed; relative equilibria are determined, and simplified reduced equations, in a linear form, are obtained. These linear reduced equations demonstrate spacecraft controllability properties. It is shown that certain maneuvers, involving a change in orbit, can be accomplished using only attitude and shape control inputs. The proposed framework can be used to study this propulsion force approach to orbital maneuvers.