Zermelo Navigation Problems on Surfaces of Revolution and Geometric Optimal Control - Algorithmes Parallèles et Optimisation Access content directly
Journal Articles ESAIM: Control, Optimisation and Calculus of Variations Year : 2023

Zermelo Navigation Problems on Surfaces of Revolution and Geometric Optimal Control

Abstract

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 and 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)

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Cite

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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