American Institute of Mathematical Sciences

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2011, 2011(Special): 1196-1205. doi: 10.3934/proc.2011.2011.1196

Energy-minimal transfers in the vicinity of the lagrangian point $L_1$

Gautier Picot 1,

1. 

Mathematics Institute, Bourgogne University, 9 avenue Savary, 21078 Dijon

Received  July 2010 Revised  April 2011 Published  October 2011

This article deals with the problem of computing energy-minimal trajectories between the invariant manifolds in the neighborhood of the equilibrium point $L_1$ of the restricted 3-body problem. Initializing a simple shooting method with solutions of the corresponding linear optimal control problem, we numerically compute energy-minimal extremals from the Pontryagin's Maximum principle, whose optimality is ensured thanks to the second order optimality condition.
Keywords: 3-body problem, numerical analysis methods, Optimal control.
Mathematics Subject Classification: Primary: 49K15, 49M05; Secondary: 70F07.
Citation: Gautier Picot. Energy-minimal transfers in the vicinity of the lagrangian point $L_1$. Conference Publications, 2011, 2011 (Special) : 1196-1205. doi: 10.3934/proc.2011.2011.1196
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