Optimization of Perturbed Spacecraft Trajectories Using Complex Dual Numbers. Part 1: Theory and Method

The problem of optimization of perturbed trajectories of spacecraft with finite thrust is considered. The problem is solved using an indirect approach based on the application of the necessary optimality conditions in the form of the maximum principle, the continuation method, and complex dual numbers for high-precision calculation of the necessary derivatives of complicated real functions of state variables. The goal of optimization is to calculate trajectories with minimal fuel consumption at a fixed angular distance and free transfer duration. A mathematical model of the spacecraft motion in equinoctial elements with an angular independent variable is used. A mathematical model of the motion, the derivation of the necessary optimality conditions, and a description of the method for solving the problem are given.