Necessary conditions for singular arcs involving multiple gravitational bodies

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

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

3 Citations (Scopus)

Abstract

We analyze the optimality of intermediate thrust arcs (singular arcs) of a rocket trajectory subject to gravitational forces from multiple bodies. We derive a series of necessary conditions for optimality including the generalized Legendre-Clebsche condition. We validate our derivations by showing that they are identical to Lawden's classical result if the equations of motion are reduced for a central gravitational field. As a means to illustrate the practical nature of our results, we apply them to a Moon-Earth transfer trajectory problem and show that the extremal solution is bang-singular-bang.

Original languageEnglish
Title of host publicationSpaceflight Mechanics 2010 - Advances in the Astronautical Sciences
Subtitle of host publicationProceedings of the AAS/AIAA Space Flight Mechanics Meeting
Pages107-121
Number of pages15
Publication statusPublished - 2010 Dec 1
EventAAS/AIAA Space Flight Mechanics Meeting - San Diego, CA, United States
Duration: 2010 Feb 142010 Feb 17

Publication series

NameAdvances in the Astronautical Sciences
Volume136
ISSN (Print)0065-3438

Other

OtherAAS/AIAA Space Flight Mechanics Meeting
CountryUnited States
CitySan Diego, CA
Period10/2/1410/2/17

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All Science Journal Classification (ASJC) codes

  • Aerospace Engineering
  • Space and Planetary Science

Cite this

Park, C., Ross, I. M., Yan, H., & Gong, Q. (2010). Necessary conditions for singular arcs involving multiple gravitational bodies. In Spaceflight Mechanics 2010 - Advances in the Astronautical Sciences: Proceedings of the AAS/AIAA Space Flight Mechanics Meeting (pp. 107-121). (Advances in the Astronautical Sciences; Vol. 136).