Optimal trajectories for aeroassisted, coplanar orbital transfer
type: Item
instance of: scholarly article
title: Optimal trajectories for aeroassisted, coplanar orbital transfer
zbMATH Open document ID: 0579.49005
DOI: 10.1007/BF00938462
author: B. George
published in: Journal of Optimization Theory and Applications
publication date: 1987-01-01T00:00:00Z
review text: This paper considers both classical and minimax problems of optimal control which arise in the study of aeroassisted, coplanar orbital transfer. The maneuver considered involves the coplanar transfer from a high planetary orbit to a low planetary orbit. An example is the HEO-to- LEO transfer of a spacecraft, where HEO denotes high Earth orbit and LEO denotes low Earth orbit. In particular, HEO can be GEO, a geosynchronous Earth orbit. The basic idea is to employ the hybrid combination of propulsive maneuvers in space and aerodynamic maneuvers in the sensible atmosphere. Hence, this type of flight is also called synergetic space flight. With reference to the atmospheric part of the maneuver, trajectory control is achieved by means of lift modulation. The presence of upper and lower bounds on the lift coefficient is considered. Within the framework of classical optimal control, the following problems are studied: (P1) minimize the energy required for orbital transfer; (P2) minimize the time integral of the heating rate; (P3) minimize the time of flight during the atmospheric portion of the trajectory; (P4) maximize the time of flight during the atmospheric portion of the trajectory; (P5) minimize the time integral of the square of the path inclination; and (P6) minimize the sum of the squares of the initial and final path inclinations. Problems (P1) through (P6) are Bolza problems of optimal control. Within the framework of minimax optimal control, the following problems are studied: (Q1) minimize the peak heating rate; (Q2) minimize the peak dynamic pressure; and (Q3) minimize the peak altitude drop. Problems (Q1) through (Q3) are Chebyshev problems of optimal control, which can be converted into Bolza problems by suitable transformations. Numerical solutions for problems (P1)-(P6) and problems (Q1)-(Q3) are obtained by means of the sequential gradient-restoration algorithm for optimal control problems. The engineering implications of these solutions are discussed. I…
Mathematics Subject Classification ID: 49J15
Mathematics Subject Classification ID: 90C52
Mathematics Subject Classification ID: 93C15
Mathematics Subject Classification ID: 49J35
Mathematics Subject Classification ID: 70M20
Mathematics Subject Classification ID: 65K10
zbMATH DE Number: 3927754
zbMATH Keywords: aeroassisted, coplanar orbital transfer
zbMATH Keywords: synergetic space flight
zbMATH Keywords: Bolza problems
zbMATH Keywords: minimax optimal control
zbMATH Keywords: Chebyshev problems
zbMATH Keywords: sequential gradient-restoration algorithm
MaRDI profile type: Publication
cites work: Approximate solutions to minimax optimal control problems for aeroassisted orbital transfer
cites work: The calculus of variations and optimal control. An introduction
cites work: Q3264687
cites work: Q3875412
cites work: Sequential gradient-restoration algorithm for optimal control problems
cites work: Sequential gradient-restoration algorithm for optimal control problems with nondifferential constraints
cites work: Recent advances in gradient algorithms for optimal control problems
cites work: Sequential gradient-restoration algorithm for optimal control problems with general boundary conditions
cites work: Method of particular solutions for linear, two-point boundary-value problems
cites work: Modified quasilinearization method for solving nonlinear, two-point boundary-value problems
cites work: General technique for solving nonlinear, two-point boundary-value problems via the method of particular solutions
cites work: Minimax Problems with Unilateral Curves in the Calculus of Variations
cites work: A Chebyshev minimax technique oriented to aerospace trajectory optimization problems.
cites work: A minimax optimal control problem
cites work: A property of an autonomous minimax optimal control problem
cites work: Numerical solution of minimax problems of optimal control. I
cites work: Numerical solution of minimax problems of optimal control. II
cites work: Optimal trajectories for aeroassisted orbital transfer
cites work: Q3286130
cites work: Optimal trajectories for aeroassisted, noncoplanar orbital transfer
full work available at URL: https://doi.org/10.1007/bf00938462
OpenAlex ID: W2005987846
description: scientific article; zbMATH DE number 3927754