Zermelo navigation on the sphere with revolution metrics - Algorithmes Parallèles et Optimisation Access content directly
Book Sections Year : 2024

Zermelo navigation on the sphere with revolution metrics

Abstract

In this article motivated by physical applications, the Zermelo navigation problem on the two-dimensional sphere with a revolution metric is analyzed within the framework of minimal time optimal control. The Pontryagin maximum principle is used to compute extremal curves and a neat geometric frame is introduced using the Carathéodory-Zermelo-Goh transformation. Assuming that the current is of revolution, the geodesics are sorted according to a Morse-Reeb classification. We then illustrate the relevance of this classification using various examples from physics: the Lindblad equation in quantum control, the averaged Kepler case in space mechanics and the Landau-Lifshitz equation in ferromagnetism.
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hal-04433828 , version 1 (02-02-2024)

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  • HAL Id : hal-04433828 , version 1

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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⟩
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