Trajectory generation using a modified simple shooting method

In this paper, we combine the theoretical result of Pontryagin´s minimum principle and a new numerical method to obtain a fast algorithm for the trajectory design problem for a reusable launch vehicle. We work with the outer-loop equations for an aircraft and consider the angle-of-attack to be the input. We cast the trajectory design problem as an optimal control problem and use Pontryagin´s minimum principle to obtain first order necessary conditions. These are in the form of a two-point boundary-value problem (TPBVP) and we solve them by means of the modified simple shooting method (MSSM). In recent work, the MSSM has been shown to be superior, both in speed and accuracy, for TPBVPs.