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

Chandeok Park, I. Michael Ross, Qi Gong, Hui Yan

Research output: Chapter in Book/Report/Conference proceedingConference contribution

9 Citations (Scopus)

Abstract

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.

Original languageEnglish
Title of host publication2010 49th IEEE Conference on Decision and Control, CDC 2010
Pages5816-5821
Number of pages6
DOIs
Publication statusPublished - 2010 Dec 1
Event2010 49th IEEE Conference on Decision and Control, CDC 2010 - Atlanta, GA, United States
Duration: 2010 Dec 152010 Dec 17

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

Other2010 49th IEEE Conference on Decision and Control, CDC 2010
CountryUnited States
CityAtlanta, GA
Period10/12/1510/12/17

Fingerprint

Moon
Rockets
Equations of motion
Optimality
Gravitation
Arc of a curve
Earth (planet)
Trajectories
Singular Control
Necessary Conditions
Extremal Solutions
Legendre
Explicit Formula
Equations of Motion
Gravity
Optimal Control
Trajectory
Series

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modelling and Simulation
  • Control and Optimization

Cite this

Park, C., Ross, I. M., Gong, Q., & Yan, H. (2010). Necessary conditions for singular arcs for general restricted multi-body problem. In 2010 49th IEEE Conference on Decision and Control, CDC 2010 (pp. 5816-5821). [5717305] (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2010.5717305
Park, Chandeok ; Ross, I. Michael ; Gong, Qi ; Yan, Hui. / Necessary conditions for singular arcs for general restricted multi-body problem. 2010 49th IEEE Conference on Decision and Control, CDC 2010. 2010. pp. 5816-5821 (Proceedings of the IEEE Conference on Decision and Control).
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Park, C, Ross, IM, Gong, Q & Yan, H 2010, Necessary conditions for singular arcs for general restricted multi-body problem. in 2010 49th IEEE Conference on Decision and Control, CDC 2010., 5717305, Proceedings of the IEEE Conference on Decision and Control, pp. 5816-5821, 2010 49th IEEE Conference on Decision and Control, CDC 2010, Atlanta, GA, United States, 10/12/15. https://doi.org/10.1109/CDC.2010.5717305

Necessary conditions for singular arcs for general restricted multi-body problem. / Park, Chandeok; Ross, I. Michael; Gong, Qi; Yan, Hui.

2010 49th IEEE Conference on Decision and Control, CDC 2010. 2010. p. 5816-5821 5717305 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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N2 - 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.

AB - 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.

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Park C, Ross IM, Gong Q, Yan H. Necessary conditions for singular arcs for general restricted multi-body problem. In 2010 49th IEEE Conference on Decision and Control, CDC 2010. 2010. p. 5816-5821. 5717305. (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2010.5717305