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Solution of the exact equations for three-dimensional atmospheric entry using directly matched asymptotic expansions
TLDR
In this paper, the exact equations of motion for three-dimensional, aerodynamically affected flight are derived and the equations are transformed into a set suitable for analytic integration using asymptotic expansions.Abstract:
The problem of determining the trajectories, partially or wholly contained in the atmosphere of a spherical, nonrotating planet, is considered. The exact equations of motion for three-dimensional, aerodynamically affected flight are derived. Modified Chapman variables are introduced and the equations are transformed into a set suitable for analytic integration using asymptotic expansions. The trajectory is solved in two regions: the outer region, where the force may be considered a gravitational field with aerodynamic perturbations, and the inner region, where the force is predominantly aerodynamic, with gravity as a perturbation. The two solutions are matched directly. A composite solution, valid everywhere, is constructed by additive composition. This approach of directly matched asymptotic expansions applied to the exact equations of motion couched in terms of modified Chapman variables yields an analytical solution which should prove to be a powerful tool for aerodynamic orbit calculations.read more
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Singular Perturbations and Time Scales in Guidance and Control of Aerospace Systems: A Survey
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Asymptotic Analysis of Quasi-Equilibrium Glide in Lifting Entry Flight
TL;DR: In this article, the authors present a formal analysis to quasi-equilibrium entry flight in a class of regular perturbation problems and obtain solutions in asymptotic expansions.
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Research and design for lifting reentry
TL;DR: In this paper, the authors considered the design of realistic configurations having partly or wholly concave undersurfaces and showed that a high-wing orbiter with moderate anhedral and a partly concave under-surface can provide about 20 % higher CL at the same angle of attack, Mach number and lift/drag ratio.
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Improved matched asymptotic solutions for three-dimensional atmospheric skip trajectories
Zeal-Sain Kuo,Nguyen X. Vinh +1 more
TL;DR: In this article, an improved technique for matching the asymptotic solutions of nonlinear differential equations is presented and successfully applied to the three-dimensional atmospheric skip trajectories, where the endpoint boundaries are artie cially extended or constructed to strengthen the physical assumptions on the outer and inner expansions for matching.
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Optimal aerodynamic control by matched asymptotic expansions
Fred Frostic,Nguyen X. Vinh +1 more
TL;DR: In this paper, the optimal lift and bank modulation of a reentry vehicle using the method of matched asymptotic expansions is presented. But it is only for the inner region, where gravity is predominant, and only four of the five adjoint equations for the free time problem have been integrated in closed form.