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Article Dans Une Revue ESAIM: Control, Optimisation and Calculus of Variations Année : 2023

Zermelo Navigation Problems on Surfaces of Revolution and Geometric Optimal Control

Résumé

In this article, the historical study from Carathéodory-Zermelo about computing the quickest nautical path is generalized to Zermelo navigation problems on surfaces of revolution, in the frame of geometric optimal control. Using the Maximum Principle, we present two methods dedicated to analyzing the geodesic flow and to compute the conjugate and cut loci. We apply these calculations to investigate case studies related to applications in hydrodynamics, space mechanics and geometry.
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Dates et versions

hal-03209491 , version 1 (27-04-2021)
hal-03209491 , version 2 (07-05-2021)
hal-03209491 , version 3 (31-03-2022)
hal-03209491 , version 4 (07-03-2023)
hal-03209491 , version 5 (04-07-2023)

Identifiants

Citer

Bernard Bonnard, Olivier Cots, Boris Wembe. Zermelo Navigation Problems on Surfaces of Revolution and Geometric Optimal Control. ESAIM: Control, Optimisation and Calculus of Variations, 2023, 29 (60), pp.34. ⟨10.1051/cocv/2023052⟩. ⟨hal-03209491v5⟩
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