Fuel-optimal rendezvous for linearized equations of motion

A new transformation of the state variables is presented so that some recent necessary and sufficient conditions for solution of the general fuel-optimal linear problem can be efficiently applied. Additional insight into the solution of the boundary-value problem may be obtained by working in this transformed state space. The necessity of inverting a fundamental matrix solution is avoided in this approach. This theory is applied to the problem of rendezvous of a spacecraft near an arbitrary Keplerian orbit in fixed time. Bounded-thrust fuel-optimal spacecraft trajectories are compared for elliptical, parabolic, and hyperbolic orbits.