COMBINED LONG DURATION FINITE BURNS AND GRAVITY ASSIST INTERPLANETARY TRAJECTORIES USING AN INDIRECT METHOD WITH ANALYTICAL GRADIENTS

摘要

A procedure for calculating the analytical derivatives required for an indirect optimization method of combined, long duration finite burn and multiple gravity assist trajectories is presented. The analytical derivatives are calculated using the state transition matrix associated with the complete set of the Euler-Lagrange equations of the optimal control problem on each trajectory segment as well as a state transition matrix that maps perturbations across any discontinuities in the state due to a flyby or impulsive maneuver. As an application, the method is used to find Earth to Saturn trajectories that use combined low thrust and gravity assists.