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Optimal trajectories based on linear equations

Author
Carter, Thomas E.
Published
Dec 1, 1990.
Physical Description
1 electronic document
Online Version

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Unclassified, Unlimited, Publicly available.
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Summary
The Principal results of a recent theory of fuel optimal space trajectories for linear differential equations are presented. Both impulsive and bounded-thrust problems are treated. A new form of the Lawden Primer vector is found that is identical for both problems. For this reason, starting iteratives from the solution of the impulsive problem are highly effective in the solution of the two-point boundary-value problem associated with bounded thrust. These results were applied to the problem of fuel optimal maneuvers of a spacecraft near a satellite in circular orbit using the Clohessy-Wiltshire equations. For this case two-point boundary-value problems were solved using a microcomputer, and optimal trajectory shapes displayed. The results of this theory can also be applied if the satellite is in an arbitrary Keplerian orbit through the use of the Tschauner-Hempel equations. A new form of the solution of these equations has been found that is identical for elliptical, parabolic, and hyperbolic orbits except in the way that a certain integral is evaluated. For elliptical orbits this integral is evaluated through the use of the eccentric anomaly. An analogous evaluation is performed for hyperbolic orbits.
Other Subject(s)
Collection
NASA Technical Reports Server (NTRS) Collection.
Note
Document ID: 19910007792.
Accession ID: 91N17105.
NASA, Goddard Space Flight Center, Flight Mechanics(Estimation Theory Symposium, 1990; p 539-556.
Terms of Use and Reproduction
No Copyright.
View MARC record | catkey: 15682685