Multibody spacecraft are used in a wide range of applications in near-Earth space, from manned space stations to unmanned space telescopes. Such systems cannot be modeled as point mass particles. Their dynamics are quite complex, being characterized by linear and nonlinear coupling between different degrees of freedom. This work explores how such dynamical coupling can be used to make changes in orbit and attitude using internal motions in a controlled manner. The methods outlined here lead to control maneuvers for multibody spacecraft without using chemical fuel. With increasing risks to space assets in Earth orbits from space debris, such control methods are both timely and valuable.