| This study uses and extends primer vector theory to obtain a minimum-fuel two or multiple impulse solution for co-planar and non co-planar elliptic-to-elliptic, time-fixed rendezvous. Lawden's conditions for an optimal impulsive trajectory and three additional methods to improve the non-optimal multiple impulse are introduced. To extend a 3-Impulse differential cost function provided by Jezewski and Rozendaal, the general differential cost function for an N-Impulse trajectory is developed. This approach defines the gradient vector for any set of boundary conditions. To determine the number of impulses, times and locations for multiple-impulse optimal trajectories automatically, a computer program is developed. This software has been thoroughly tested on a wide variety of rendezvous situations. The singularity for a transfer angle of 180{dollar}spcirc{dollar} and the singular case of sin I = 0 are also accounted for in the program. Part of this work was accomplished using the Generalized Reduced Gradient method using its associated GRG2 computer code. The effects of inclination between the vehicle and target orbits, the initial positions of the vehicle and target, and the direction of the major axes are considered. Numerical results for several different orbit configurations are produced and discussed. The results are compared with the Hohmann/Hohmann type transfer and/or the optimal, finite, three-impulse transfer. |
