An intrinsic formulation of geometric proportional-derivative tracking control for fully actuated mechanical systems is developed. The region of stability is determined directly from the size of the system's injectivity radius and, for a restricted set of control problems, the system's locus of cut points about a desired reference point. Exponential stability is obtained under certain boundedness conditions. For controlled motion along a geodesic, the proffered scheme yields a particularly simple and elegant manifestation of the underlying use of the mass-spring-damper paradigm in the control design methodology. (C) 2011 Elsevier Ltd. All rights reserved.