Real-time trajectory optimization is a crucial aspect of aerospace applications, particularly for atmospheric re-entry missions. Since in this phase space vehicles are subject to disturbances or mission changes during flight, a trajectory replanning module is generally used to compute corrections within computational time and resources. Analytical guidance laws meet these requirements without resorting to solve large numerical optimization problems associated with direct methods or indirect methods, which are highly sensitive to initialization. One method of deriving such analytical guidance laws is the application of the Pontryagin Maximum Principle, which provides the necessary conditions for a control to be optimal. However, for nonlinear dynamics, the resulting equations are difficult to solve analytically and require numerically solving a two-point boundary value problem in most cases. Approximation methods, in particular asymptotic expansions, have been used to obtain analytical solutions for this application. A preliminary step to obtain solutions of the optimal control problem is to compute the analytical solutions of the equations of motion for the uncontrolled system. This work then focuses on solving the equations of motion using a more complex aerodynamic model than those reported in the literature.
Ramírez et al. (Wed,) studied this question.