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

摘要

An investigation of the question of existence of solutions of a planar optimalimpulsive rendezvous in a Newtonian gravitational field reveals that if the initialand terminal angular momentum are positive, either a solution exists, orelse an approximate solution exists to any degree of accuracy. If the differencesin the values of the orbital angle where the velocity increments are appliedare not integer multiples of π then an actual solution exists, not an approximateone. Under these conditions, necessary and sufficient conditions foroptimality are available. The question of realizability of solutions is discussed.An example is presented of a two-impulse rendezvous between the apogees oftwo identical ellipses having a common center of attraction but different inclination.This example illustrates existence, approximate solutions, and realizabilityof solutions.