A nonlinear programming approach for optimizing two-stage lifting vehicle ascent to orbit

An optimal atmospheric flight branched trajectory-shaping capability is presented based on the Davidon-Fletcher-Powell variable metric parameter optimization technique. Gradient information is generated using finite difference methods. A typical atmospheric flight branched optimization problem is analyzed which requires the determination of 31 parameters. This parameter set includes the three-dimensional description of vehicle attitude control angles for three branches of flight: first-stage ascent, second-stage ascent, and first-stage flyback. The important inflight inequality contraints required to maintain the integrity of the vehicles are considered. Some of the numerical methods employed are discussed, along with several new auxiliary techniques developed to improve the compatibility of the numerical gradient and iterator.