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

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