Zermelo navigation problems on surfaces of revolution and geometric optimal control

被引：0
作者：
Bonnard, Bernard [1 ,2 ]
Cots, Olivier [3 ]
Wembe, Boris [3 ]
机构：
[1] INRIA Sophia Antipolis, McTAO team, Valbonne, France
[2] UBFC, Inst Math Bourgogne, Besancon, France
[3] ENSEEIHT, IRIT, Toulouse, France
来源：
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2023年 / 29卷
关键词：
Zermelo navigation problems; optimal control; abnormal geodesics; conjugate and cut loci; regularity of the value function; CUT LOCI; CONJUGATE; 2-SPHERE; SYSTEMS;
D O I：
10.1051/cocv/2023052
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this article, the historical study from Caratheodory-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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页码：376 / 814
页数：34
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