The aim of this thesis is to review and further investigate orbital maneuvers on satellite flight formations using relative orbital elements. The study of flight formations applies to twin satellites as well as swarms and constellations of thousands of them, with applications from autonomous rendezvous and docking maneuvers of manned spacecrafts, to Earth and deep space observation through swarms of satellites acting as a virtual radar dish, overcoming the difficulties associated with big, single satellite missions. After proposing the derivation of the state transition matrices that model the perturbed orbital dynamics, maneuvering schemes found in literature are employed to solve formation reconfiguration problems, highlighting particularly economic or optimal strategies.