Properties of the optimal trajectories for coplanar, aeroassisted orbital transfer
type: Item
instance of: scholarly article
title: Properties of the optimal trajectories for coplanar, aeroassisted orbital transfer
zbMATH Open document ID: 0724.49024
DOI: 10.1007/BF00940459
author: D. Kharzeev
published in: Journal of Optimization Theory and Applications
publication date: 1991-01-01T00:00:00Z
review text: This paper is concerned with the optimization of trajectories for coplanar, aeroassisted orbital transfer (AOT) from a high Earth orbit (HEO) to a low Earth orbit (LEO). In particular, HEO can be a geosynchronous Earth orbit (GEO). It is assumed that the initial and final orbits are circular, that the gravitational field is central and is governed by the inverse square law, and that two impulses are employed, one at HEO exit and one at LEO entry. During the atmospheric pass, the trajectory is controlled via the lift coefficient in such a way that the total characteristic velocity is minimized. First, an ideal optimal trajectory is determined analytically for lift coefficient unbounded. This trajectory is called grazing trajectory, because the atmospheric pass is made by flying at constant altitude along the edge of the atmosphere until the excess velocity is depleted. For the grazing trajectory, the lift coefficient varies in such a way that the lift, the centrifugal force due to the Earth's curvature, the weight, and the Coriolis force due to the Earth's rotation are in static balance. Also, the grazing trajectory simultaneously minimizes/nearly minimizes the total characteristic velocity/the peak values of the altitude drop, the dynamic pressure, and the heating rate. Next, starting from the grazing trajectory results, a real optimal trajectory is determined numerically for lift coefficient bounded from both below and above. This trajectory is characterized by atmospheric penetration with the smallest possible entry angle, followed by flight at the lift coefficient lower bound. Consistently with the grazing trajectory behavior, the real optimal trajectory simultaneously minimizes/nearly minimizes the total characteristic velocity/the peak values of the altitude drop, the dynamic pressure, and the heating rate.
Mathematics Subject Classification ID: 49N70
Mathematics Subject Classification ID: 49N75
Mathematics Subject Classification ID: 90C52
Mathematics Subject Classification ID: 49J15
Mathematics Subject Classification ID: 70Q05
zbMATH DE Number: 4194563
zbMATH Keywords: flight mechanics
zbMATH Keywords: astrodynamics
zbMATH Keywords: nonlinear two-point boundary-value problems
zbMATH Keywords: sequential gradient-restoration algorithm
zbMATH Keywords: aeroassisted orbital transfer (AOT)
zbMATH Keywords: grazing trajectory
MaRDI profile type: Publication
cites work: Optimal trajectories for aeroassisted orbital transfer
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cites work: Optimal trajectories for aeroassisted, coplanar orbital transfer
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full work available at URL: https://doi.org/10.1007/bf00940459
OpenAlex ID: W1976068110
description: scientific article; zbMATH DE number 4194563