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Non-integrability of the minimum-time Kepler problem

Orieux, Michaël; Caillau, Jean-Baptiste; Combot, Thierry; Féjoz, Jacques (2018), Non-integrability of the minimum-time Kepler problem, Journal of Geometry and Physics, 132, Octobre 2018, p. 452-459. 10.1016/j.geomphys.2018.06.012

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Type
Article accepté pour publication ou publié
Date
2018
Journal name
Journal of Geometry and Physics
Volume
132
Number
Octobre 2018
Publisher
Elsevier
Pages
452-459
Publication identifier
Metadata
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Author(s)
Orieux, Michaël
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Caillau, Jean-Baptiste
Laboratoire Jean Alexandre Dieudonné [JAD]
Combot, Thierry
Institut de Mathématiques de Bourgogne [Dijon] [IMB]
Féjoz, Jacques
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Institut de Mécanique Céleste et de Calcul des Ephémérides [IMCCE]
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.
Subjects / Keywords
Hamiltonian systems; Integrability; Differential Galois theory; Optimal control; Kepler problem