Volume 29, 2023
|Number of page(s)||34|
|Published online||31 July 2023|
Zermelo navigation problems on surfaces of revolution and geometric optimal control
1 INRIA Sophia Antipolis, McTAO team, Valbonne, France
2 Institut de Mathématiques de Bourgogne, UBFC, France
3 ENSEEIHT, IRIT, Toulouse, France
* Corresponding author: firstname.lastname@example.org
Accepted: 1 July 2023
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.
Mathematics Subject Classification: 49K15 / 53C60 / 70H05
Key words: Zermelo navigation problems / optimal control / abnormal geodesics / conjugate and cut loci / regularity of the value function
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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