Thrust - Limited Optimal Three - Dimensional Spacecraft Trajectories

Abstract

Several optimal three-dimensional orbital transfer problems are solved for thrust-limited spacecrafts using collocation and nonlinear programming techniques. The solutions for full nonlinear equations of motion are obtained where the integrals of the free Keplerian motion in three dimensions are utilized for coasting arcs. In order to limit the solution space, interior-point constraints are used which proved to be beneficial in finding the optimal results by making initial estimates more sensible. The application of this methodology to the design of several three dimensional optimal trajectories is also investigated. The results indicate that the method is suitable for any 3D transfer between noncoplanar and non-coaxial orbits.