Thrust-limited optimal three-dimensional spacecraft trajectories

摘要

Using a newly developed direct optimization scheme. several optimal three dimensional orbital transfer problems are solved for the thrust-limited spacecraft. The methodology of direct collocation and nonlinear programming is followed in a way which permits analytical evaluation of the resulting Jacobian and Hessian matrices. The solution to the full nonlinear equations of motion is obtained where the integrals of the free Keplerian motion in three dimensions are utilized for the coast arcs. 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. Application of this methodology to the design of several three dimensional optimal trajectories was investigated. The results indicate this method to be suitable for any 3D transfer maneuver between non-coplanar and non-coaxial orbits.