Orbit transfer and rendezvous is an essential component of all space missions. This dissertation surveys the published literature on methods for optimizing impulsive orbit transfer, investigates the use of a new orbit state representation for this purpose, and finally introduces and tests a method for executing orbit transfer and rendezvous using this orbit representation. Existing methods have used primer vector theory as a basis for indirect optimization and geometric orbit representations to construct and then optimize transfer trajectories. Both approaches have their advantages and disadvantages. The orbit state representation introduced here uses angular momentum, energy, and eccentricity. These quantities fully define an orbit and can be mapped onto the Keplerian orbital elements, and they have several useful characteristics as the basis for a control algorithm - they are nonsingular, stationary in steady state, and have relatively simple dynamics. While minimizing control effort in these variables does not correspond perfectly to impulse/∆V, the difference is generally quite small and can be used as a starting point for finding the minimum-∆V trajectory. With proper care, a control method that is as efficient as unlimited thrust impulsive maneuvers is designed utilizing this representation.