We may find here some resources about the averaged kepler problem with current. This problem is part of time minimal optimal control problems and more particularly, it may be seen as a Zermelo navigation problem on the sphere.
Please visit the online documentation to explore the optimal synthesis. All the codes to make the visualizations may be found here. We refer to this article1 for more details about Zermelo navigation on the sphere with revolution metrics.
Footnotes
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Bernard Bonnard, Olivier Cots, Yannick Privat, Emmanuel Trélat. Zermelo navigation on the sphere with revolution metrics. IVAN KUPKA LEGACY: A Tour Through Controlled Dynamics, 12, pp.35--66, 2024, AIMS Applied Math Books - Special issue in honor of I. Kupka, ISBN-10: 1-60133-026-X ISBN-13: 978-1-60133-026-0. ⟨hal-04433828⟩ ↩