A Semi-Analytic Approach for Trajectory Design Optimization Using Linearized Equations of Motion

A Semi-Analytic Approach is presented in this paper for the problem of low-thrust trajectory design optimization in a two body domain under the assumption of a constant thrust acceleration magnitude. The key innovation in this proposed approach is using the linearized Hill-Clohessy-Wiltshire equations of motion for orbit raising and rendezvous maneuvers. Successive reference orbits are assumed, and a trajectory is optimized in the vicinity of each reference orbit. An indirect approach is adopted to write the necessary optimality conditions and derive a control law analytically. Numerical case studies are presented.