ISSN:
1573-2878
Keywords:
Orbital transfer
;
coplanar orbital transfer
;
aeroassisted orbital transfer
;
transfer between circular orbits
;
grazing trajectories
;
nearly-grazing trajectories
;
optimal trajectories
;
lift modulation
;
Bolza problems
;
Chebyshev problems
;
minimax problems
;
numerical methods
;
computing methods
;
transformation techniques
;
sequential gradient-restoration algorithm
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract 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 entry and exit 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. In particular, the merits of nearly-grazing trajectories are considered.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00938462
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