New numerical methods for determining periodic orbits in the circular restricted three-body problem

M. Pontani, C. Martin, Bruce A Conway

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

Abstract

The generation of periodic orbits in the context of the circular restricted three-body problem has been pursued with different approaches, for decades. The equations of motion for the problem at hand are not amenable to an analytical solution, and therefore past studies are mostly focused on analytical approximations, shooting algorithms, and generating functions. These techniques exhibit limitations due to the high sensitivity to the starting guess or to the reduced spatial range of applicability. This paper formulates the problem of determining periodic orbits as an optimal control problem, and applies two distinct methods to its solution. The first method is the particle swarm optimization technique, which is a stochastic, population-based methodology inspired by the unpredictable motion of bird flocks. The second method is represented by the direct transcription with nonlinear programming algorithm, which is based on the conversion of the original problem into a nonlinear programming problem. This research describes these two novel approaches to determining periodic orbits, their respective favorable features, and their drawbacks.

Original languageEnglish (US)
Title of host publication61st International Astronautical Congress 2010, IAC 2010
Pages499-509
Number of pages11
StatePublished - Dec 1 2010
Event61st International Astronautical Congress 2010, IAC 2010 - Prague, Czech Republic
Duration: Sep 27 2010Oct 1 2010

Publication series

Name61st International Astronautical Congress 2010, IAC 2010
Volume1

Other

Other61st International Astronautical Congress 2010, IAC 2010
CountryCzech Republic
CityPrague
Period9/27/1010/1/10

ASJC Scopus subject areas

  • Aerospace Engineering
  • Astronomy and Astrophysics

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