This thesis develops an analytical dynamics-based approach for simultaneous position and orientation tracking control of a chaser spacecraft with respect to an uncontrolled target spacecraft. The control requirements are formulated as holonomic or non-holonomic constraints, which are differentiated to obtain a constraint equation linear in acceleration. Exact real-time control forces are then generated by substituting the control constraints into the Udwadia-Kalaba equation. Three major contributions are presented. Firstly, the complete six-degree-of-freedom formulation of the Udwadia-Kalaba based pose tracking controller is presented. Simulations demonstrate the achievement of the desired objectives in space. Subsequently, a planar pose tracking controller is formulated for both a single and dual chaser configuration. Simulation results highlight the planar position and orientation synchronization with respect to a spinning target. Finally, the controller is experimentally validated in the Spacecraft Proximity Operations Testbed at Carleton University. Results show that the pose tracking control objective is achieved.