Solution of Transformed Reentry Equations for Variable Lift and Roll Angle by Matched Asymptotic Expansion

This paper presents a new method for the optimization of the three-dimensional atmospheric entry equations. The procedure is based on the Matched Asymptotic Expansion (MAE) method, one of the Singular Perturbation Theory (SPT) procedures, and is aided with the Variation of Extremals (VOE) method. The new technique offers a very low solution time and an acceptable accuracy compared with the other numerical methods used until now for reentry optimization. Furthermore, it permits considering both the lift and the aerodynamic roll angle as control variables. The features of the new method appear completely suitable to develop a guidance scheme for atmospheric reentry.