Optimization of launch vehicle ascent trajectories with path constraints and coast arcs

This paper describes improvements made to a hybrid analytic/numerical algorithm for optimization of launch vehicle trajectories. Modifications are described that improve the accuracy of the solution. In addition, the algorithm has been extended to include path constraints for normal force and angle of attack, and the terminal constraints have been generalized to allow optimal attachment to a target orbit defined by inclination, apogee radius, and perigee radius. Singularities that occur for circular orbits and for equatorial orbits are identified. Finally, necessary conditions are derived and applied for the introduction of coasting arcs that are typically required for a great variety of missions. To verify the algorithm presented in this paper, results of a test mission to a 100-nm circular equatorial orbit have been compared with two other independent optimization codes.