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

Pages: 1196 - 1205, Issue Special, September 2011

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Gautier Picot - Mathematics Institute, Bourgogne University, 9 avenue Savary, 21078 Dijon, France (email)

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.

Keywords:  Optimal control, 3-body problem , numerical analysis methods
Mathematics Subject Classification:  Primary: 49K15, 49M05; Secondary: 70F07

Received: July 2010;      Revised: April 2011;      Published: October 2011.