Nonplanar Trajectory Optimization with Variable Specific Impulse Engine Using Gauss Pseudospectral Method

Abstract—Nonplanar trajectory optimization problem with advanced variable specific impulse magnetoplasma rocket (VASIMR) engine is studied. A newly developed method called Gauss Pseudospectral method is applied to the nonplanar trajectory optimization problem with VASIMR engine. Three representative trajectory optimization problems are solved. The first is an orbit raising problem from LEO to GEO; the second is a transfer from LEO to Sun synchronous orbit with large inclination change; the third is a transfer from LEO to Molniya orbit. These three problems demonstrate the ability of VASIMR and Gauss Pseudospectral method to deal with different kind of trajectory optimization problems. The results show that VASIMR engine can greatly increase the payload ratio for its large specific impulse and can be applied in different kinds of orbital transfer problems. It also demonstrates the Gauss Pseudospectral method is a powerful and effective method to deal with complicated trajectory optimization problems. Especially it can catch the proper switching structure without solving the difficult two point boundary problem. The purpose of this paper is trying to make a contribution to different kinds of orbital transfer with VASIMR engine using Gauss Pseudospectral method. Index Terms—trajectory optimization, variable specific