Necessary conditions for singular arcs for general restricted multi-body problem

We analyze the optimality of intermediate thrust arcs (singular arcs) of a rocket trajectory subject to multiple gravitational bodies in the restricted multi-body problem. We derive a series of necessary conditions for optimality including the generalized Legendre-Clebsch condition, and an explicit...

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Bibliographic Details
Published in49th IEEE Conference on Decision and Control (CDC) pp. 5816 - 5821
Main Authors Chandeok Park, Ross, I Michael, Qi Gong, Hui Yan
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.12.2010
Subjects
Equations
Gravity
Moon
Rockets
Space vehicles
Switches
Trajectory
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Summary:We analyze the optimality of intermediate thrust arcs (singular arcs) of a rocket trajectory subject to multiple gravitational bodies in the restricted multi-body problem. We derive a series of necessary conditions for optimality including the generalized Legendre-Clebsch condition, and an explicit formula for the singular optimal control law. Our derivations become identical to Lawden's classical result if the equations of motion are reduced for a central gravity field. As a means to illustrate the practical nature of our results, we apply them to a Moon-Earth transfer problem and show that the extremal solution is bang-singular-bang.
ISBN:142447745X
9781424477456
ISSN:0191-2216
DOI:10.1109/CDC.2010.5717305