# American Institute of Mathematical Sciences

2011, 2011(Special): 229-239. doi: 10.3934/proc.2011.2011.229

## Discrete and differential homotopy in circular restricted three-body control

 1 Math. Institute, Bourgogne Univ. & CRNS, 9 avenue Savary, F-21078 Dijon, France 2 Math. Institute, Bourgogne Univ. & CNRS, 9 avenue Savary, F-21078 Dijon, France

Received  August 2010 Revised  May 2011 Published  October 2011

The planar circular restricted three-body problem is considered. The control enters linearly in the equation of motion to model the thrust of the third body. The minimum time optimal control problem has two scalar parameters: The ratio of the primaries masses which embeds the two-body problem into the three-body one, and the upper bound on the control norm. Regular extremals of the maximum principle are computed by shooting thanks to continuations with respect to both parameters. Discrete and di erential homotopy are compared in connection with second order sucient conditions in optimal control. Homotopy with respect to control bound gives evidence of various topological structures of extremals.
Citation: Jean-Baptiste Caillau, Bilel Daoud, Joseph Gergaud. Discrete and differential homotopy in circular restricted three-body control. Conference Publications, 2011, 2011 (Special) : 229-239. doi: 10.3934/proc.2011.2011.229
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