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)


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
Number of pages15
Publication statusPublished - 2010
EventAAS/AIAA Space Flight Mechanics Meeting - San Diego, CA, United States
Duration: 2010 Feb 142010 Feb 17

Publication series

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


OtherAAS/AIAA Space Flight Mechanics Meeting
Country/TerritoryUnited States
CitySan Diego, CA

All Science Journal Classification (ASJC) codes

  • Aerospace Engineering
  • Space and Planetary Science


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