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

Gautier Picot

doi:10.3934/proc.2011.2011.1196

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2011, Volume 2011: 1196-1205. Doi: 10.3934/proc.2011.2011.1196 open access

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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: August 2017

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Abstract

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.

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Mathematics Subject Classification: Primary: 49K15, 49M05; Secondary: 70F07.

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