Optimal aerodynamic control by matched asymptotic expansions

Abstract

This paper presents the solution for the optimal lift and bank modulation of a reentry vehicle using the method of matched asymptotic expansions. The solution, which contains all effects of aerodynamic, gravitational, and centrifugal forces, is uniformly valid everywhere.The solution for the outer region, where gravitational force is predominant is obtained in closed form. To date, for the inner region, only four of the five adjoint equations for the free time problem have been integrated in closed form. The fifth equation has been integrated by considering the free range problem, or by using a linear approximation of the drag polar near the optimal lift control. By a new invariant relation, and a transformation of the fifth adjoint variable, it will be shown in this paper that, for the most general drag polar, the fifth equation can be integrated by quadrature. The equation will be completely integrated for a generalized drag polar. The inner solution will be matched with the outer solution providing a composite solution uniformly valid everywhere.