Fixed-point algorithms for optimal ascent trajectories of launch vehicles

A fixed-point formulation and the associated algorithms for rapid generation of optimal ascent trajectories of launch vehicles through the atmosphere are presented, The complete ascent trajectory is tacitly divided into an endo-atmospheric and an exo-atmospheric portion. Since the exo-atmospheric trajectory can be obtained reliably and rapidly, a special form of two-point boundary value problem (TPBVP) is formulated in the endo-atmospheric portion. This special TPBVP leads to a sequence of nested fixed-point problems. Several algorithmic options to solve these problems using modified fixed-point iterations are discussed.