USING BATTIN'S METHOD TO OBTAIN MULTIPLE-REVOLUTION LAMBERT'S SOLUTIONS

摘要

In this paper Battin's method for the Lambert's problem is extended to calculate the multiple-revolution Lambert's solutions. It is shown that the original successive substitution method described in Battin's method converges to one of the two N-revolution solution with N ≥ 1. If the order of the original successive substitution is reversed, then the reversed successive substitution converges to the other N-revolution solution. It is also shown that the original successive substitution converges to the N-revolution transfer orbit with the smaller semi-major axis, and the reversed successive substitution converges to the one with the larger semi-major axis. A preprocessing algorithm is given to provide initial guesses with the convergence of the successive substitution methods is guaranteed.