A combined gradient/neighboring extremal algorithm for the calculation of optimal transfer trajectories between noncoplanar orbits using a constant low thrust rocket

This algorithm is designed to minimize computer programming requirements while accurately satisfying the boundary conditions without prior knowledge of the solution. Initially a first order gradient technique, using a multiplier method to enforce the terminal conditions, approximately solves a coplanar problem between orbits that match those of the noncoplanar problem in all respects except for the relative inclination angle. Starting with the gradient results, a neighboring extremal technique first accurately solves the coplanar problem. It then solves the noncoplanar problem by solving a series of intermediate transfers progressively increasing the inclination angle of the terminal orbit to the desired value. Numerical examples of the application of this combined algorithm are presented and discussed. Good results have been obtained with inclination angles of the final orbit relative to the initial orbit of up to 85 deg.