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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 analyze 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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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03209491
Contributor : Olivier Cots Connect in order to contact the contributor
Submitted on : Thursday, March 31, 2022 - 4:00:45 PM
Last modification on : Monday, July 4, 2022 - 9:33:57 AM

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2022-BCW-preprint.pdf
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  • HAL Id : hal-03209491, version 3

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Bernard Bonnard, Olivier Cots, Boris Wembe. Zermelo Navigation Problems on Surfaces of Revolution and Geometric Optimal Control. 2022. ⟨hal-03209491v3⟩

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