EXISTENCE AND SUFFICIENCY CONDITIONS FOR OPTIMAL IMPULSIVE RENDEZVOUS IN A NEWTONIAN GRAVITATIONAL FIELD

An investigation of the question of existence of solutions of a planar optimal impulsive rendezvous in a Newtonian gravitational field reveals that if the initial and terminal angular momentum are positive, either a solution exists, or else an approximate solution exists to any degree of accuracy. If the differences in the values of the orbital angle where the velocity increments are applied are not integer multiples of pi then an actual solution exists, not an approximate one. Under these conditions, necessary and sufficient conditions for optimality are available. The question of realizability of solutions is discussed. An example is presented of a two-impulse rendezvous between the apogees of two identical ellipses having a common center of attraction but different inclination. This example illustrates existence, approximate solutions, and realizability of solutions.