Optimization of finite-thrust trajectories with fixed angular distance

The article presents a new approach for optimizing the trajectories of spacecraft with finite thrust. The recently proposed angular variable – the auxiliary longitude – is considered as an independent variable. The advantages of using this variable to optimize a trajectory with a fixed angular distance and free transfer duration are shown. A complete system of necessary optimality conditions for the considered representation of the optimal control problem is presented. An approach to solving the minimum-fuel problem is considered that is based on the sequential solution of the problems of optimizing the limited power trajectories and the trajectories with a constant exhaust velocity. This approach includes verifying the existence of a solution to the minimum-fuel problem by solving the thrust minimization problem. We present a method for optimization of the finite-thrust trajectories with constant exhaust velocity, based on the application of the maximum principle and the continuation method, which does not require the user to specify an initial guess for the initial values of costate variables. The article presents numerical examples to illustrate the application of such approach, and discusses the properties of the obtained optimal trajectories. © 2021 IAA