Optimization of Multi-revolution Limited Power Trajectories Using Angular Independent Variable

Optimization of low-thrust trajectories is necessary in the design of space missions using electric propulsion systems. We consider the problem of limited power trajectory optimization, which is a well-known case of the low-thrust optimization problem. In the article, we present an indirect approach to trajectory optimization based on the use of the maximum principle and the continuation method. We introduce the concept of auxiliary longitude and use it as a new independent variable instead of time. The use of equations of motion in the equinoctial elements and a new independent variable allowed us to simplify the optimization of limited power trajectories with a fixed angular distance and free transfer duration. The article presents a new form of necessary optimality conditions for this problem and describes an efficient new numerical method to solve the limited power trajectory optimization problem. We show the existence of several trajectories with a fixed transfer duration and free angular distance that satisfy the necessary optimality conditions. Using numerical examples, we confirm the existence of the limiting values of the characteristic velocity and the product of the cost function value and the transfer duration as the angular distance increases. The high computational performance of the developed technique makes it possible to carry out and present an analysis of the angular flight range and initial true longitude impact on the cost function, transfer duration, and characteristic velocity.