Improved matched asymptotic solutions for deceleration control during atmospheric entry

Abstract

An improved technique for matching the asymptotic solutions of non-linear differential equations is presented and successfully applied to the problem of evaluating the maximum deceleration during atmospheric entry of space vehicles. The classical method of matched asymptotic expansions is generally restricted to the first-order solutions, and the resulting accuracy usually depends on the physical problems. In this method the end-point boundaries are artificially extended or constructed to strengthen the physical assumptions on the outer and inner expansions for the matching while in the evaluation of the constants of integration in the composite solutions, the prescribed end points are effectively enforced. Furthermore, based on the uniformly valid first-order solutions, the linearized equations for the small discrepancies are generated and integrated separately near the boundaries to obtain the perturbed outer and inner expansion solutions for a second-order matching. The solutions obtained by this improved technique are very accurate when applied to the equations for reentry trajectories. The explicit solutions for skip trajectories and ballistic trajectories are then used for analyzing the effects of the initial speed and the initial entry angle on the maximum deceleration and maximum heating rate during entry.