INDIRECT OPTIMIZATION OF THREE DIMENSIONAL FINITE-BURNING INTERPLANETARY TRANSFERS INCLUDING SPIRAL DYNAMICS

摘要

Utilizing a step-by-step process developed previously for the two-dimensional dynamics model and using techniques for accurately estimating the unknown co-states for three-dimensional escape and capture spirals, the indirect optimization problem for a three-dimensional Low Earth Orbit (LEO) to Low Mars Orbit (LMO) transfer is solved. Minimum propellant trajectories for finite-burning engines are calculated. Solutions are considered with and without control limits on specific impulse and compared with previous research. Unlike other research, the entire trajectory, including the Martian capture sequence, is integrated in an Earth referenced frame. Additionally, the capture sequence is not found by iteratively lowering the final LMO target orbit but the desired target LMO orbit is directly solved for with no successive iterations of increasingly lower LMO orbits. As in the two-dimensional case, more fuel efficient trajectories are found for the same mission objectives and constraints as published in other research, emphasizing the importance of this technique in allowing the user to find the best local optimal solution for the capture sequence. Whereas previous research only achieved final Martian orbits of 6 Mars Radii (DU_M), the new approach finds solutions for final Martian circular orbits of 1.47-2.00 DU_M (5,000-6794 km).