Optimal impulsive space trajectories based on linear equations

Consideration is given to a problem of minimizing the total characteristic velocity of a spacecraft based on linear equations of motion and finitely many instantaneous impulses that result in velocity jump discontinuities. This formulation is flexible enough to make it possible to specify some of the impulses a priori by the mission planner. A specified set of nonlinear equations is presented for solution of the two-point boundary-value problem. These equations are found to be at most quadratic if the times of the velocity increments are specified. Several practical examples of spacecraft maneuvers and rendezvous in which the equations of motion are linear are given, including the computation of the velocity increments of a spacecraft near a real or fictitious satellite or space station in a circular or Keplerian orbit and the computation of the maneuvers of a spcecraft near a libration point in the restricted three-body problem.