"Tethered Satellite Systems (TSS) has been an ongoing project around the world for many decades. This study examined the dynamics an dcontrols of tethered satellites. The equations of motion were developed and simulated with no control and small eccentric orbits. A control law was derived by associating the Hamiltonian of the system to a Lyapunov Funciton. This control law was then simulated to demonstrate ability and robustness. The tethered system can be retrieved and deployed in a small number of orbits, and return from a perturbation quickly. Examination of a non thruster controlled system resulted in asymptotic convergence in retrieval and station keeping, but the inplane angle, orbital plane, converged during deployment. Time to complete the phases was similar to out of plane thruster controlled. The maximum eccentricities were found for retrieval and deployment when the system started at the perihelion of the orbit with a 100Km tether. Drag was added to the model because it effects the dynamics when the subsatellite is very close to earth. Most of the effects are seen in the inplane angle. At fully deployed the inplane angle was small. A Lyapunov controller for tether satellites works very well under ideal conditions. Once aerodynamics are included into the model, offsets and oscillations occur because of the new forces that unbalance the system compared to the model without drag"--Abstract.