Riemannian metric of the averaged energy minimization problem in orbital transfer with low thrust
Bernard Bonnard, Jean-Baptiste Caillau (2007)
Annales de l'I.H.P. Analyse non linéaire
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Bernard Bonnard, Jean-Baptiste Caillau (2007)
Annales de l'I.H.P. Analyse non linéaire
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A. Agrachev, B. Bonnard, M. Chyba, I. Kupka (1997)
ESAIM: Control, Optimisation and Calculus of Variations
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Ugo Boscain, Francesco Rossi (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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Fix two points and two directions (without orientation) of the velocities in these points. In this paper we are interested to the problem of minimizing the cost
along all smooth curves starting from
Chi, M.Y. (1998)
Rendiconti del Seminario Matematico
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Karsten Grove, Hermann Karcher (1973)
Compositio Mathematica
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Wilhelm Klingenberg (1979)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Igor Moiseev, Yuri L. Sachkov (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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The left-invariant sub-Riemannian problem on the group of motions of a plane is considered. Sub-Riemannian geodesics are parameterized by Jacobi's functions. Discrete symmetries of the problem generated by reflections of pendulum are described. The corresponding Maxwell points are characterized, on this basis an upper bound on the cut time is obtained.