Aas 03-568 Using Battin’s Method to Obtain Multiple-revolution Lambert’s Solutions

In this paper, Battin’s method for the Lambert’s problem is extended to calculate the multiplerevolution 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 with the convergence of the successive substitution methods is guaranteed.