In addition to the internal hinge degrees of freedom, free-flying manipulators have 6 additional degrees of freedom associated with the overall location and orientation of the manipulator. These additional 6 degrees of freedom are normally assigned to the manipulator base-body. While the base-body link is typically chosen based on de-sign and use considerations, from a more general perspective, any one of the manip-ulator links can be designated as the base-body with equal validity. This freedom of choice, not available for ground manipulators, is responsible for a base-invariance symmetry possessed by free-flying manipulators [83, 148]. In this chapter, we use this symmetry to study free-flying manipulator dynamics.