# Recent Advances in Celestial and Space MechanicsTime-Minimum Control of the Restricted Elliptic Three-Body Problem Applied to Space Transfer

Recent Advances in Celestial and Space Mechanics: Time-Minimum Control of the Restricted Elliptic... [In this chapter, we investigate time minimal transfers in the elliptic restricted 3-body problem. We study the controllability of the problem and show that it is small-time locally controllable at the equilibrium points. We present results about the structure of the extremal trajectories, based on a previous study of the time minimum control of the circular restricted 3-body problem. We use indirect numerical methods in optimal control to simulate time-minimizing space transfers using the elliptic model from the geostationary orbit to the equilibrium points L1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_1$$\end{document} and L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_2$$\end{document} in the Earth-Moon system, as well as a rendezvous mission with a near-Earth asteroid.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

# Recent Advances in Celestial and Space MechanicsTime-Minimum Control of the Restricted Elliptic Three-Body Problem Applied to Space Transfer

Part of the Mathematics for Industry Book Series (volume 23)
Editors: Bonnard, Bernard; Chyba, Monique
29 pages      Publisher
Springer International Publishing
© Springer International Publishing Switzerland 2016
ISBN
978-3-319-27462-1
Pages
179 –208
DOI
10.1007/978-3-319-27464-5_6
Publisher site
See Chapter on Publisher Site

### Abstract

[In this chapter, we investigate time minimal transfers in the elliptic restricted 3-body problem. We study the controllability of the problem and show that it is small-time locally controllable at the equilibrium points. We present results about the structure of the extremal trajectories, based on a previous study of the time minimum control of the circular restricted 3-body problem. We use indirect numerical methods in optimal control to simulate time-minimizing space transfers using the elliptic model from the geostationary orbit to the equilibrium points L1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_1$$\end{document} and L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_2$$\end{document} in the Earth-Moon system, as well as a rendezvous mission with a near-Earth asteroid.]

Published: Mar 27, 2016

Keywords: Optimal control theory; Astrodynamics; Near Earth Orbiter