Non-integrability of the minimum-time Kepler problem

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Date
2018
Dewey
Analyse
Sujet
Hamiltonian systems; Integrability; Differential Galois theory; Optimal control; Kepler problem
Journal issue
Journal of Geometry and Physics
Volume
132
Number
Octobre 2018
Publication date
10-2018
Article pages
452-459
Publisher
Elsevier
DOI
http://dx.doi.org/10.1016/j.geomphys.2018.06.012
URI
https://basepub.dauphine.fr/handle/123456789/19911
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Author
Orieux, Michaël
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Caillau, Jean-Baptiste
199970 Laboratoire Jean Alexandre Dieudonné [JAD]
Combot, Thierry
50 Institut de Mathématiques de Bourgogne [Dijon] [IMB]
Féjoz, Jacques
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
541700 Institut de Mécanique Céleste et de Calcul des Ephémérides [IMCCE]
Type
Article accepté pour publication ou publié
Abstract (EN)
We prove, using Moralès–Ramis theorem, that the minimum-time controlled Kepler problem is not meromorphically integrable in the Liouville sens on the Riemann surface of its Hamiltonian.