Abnormal Geodesics in 2D-Zermelo Navigation Problems in the Case of Revolution and the Fan Shape of the Small Time Balls
Bernard Bonnard,
Olivier Cots,
Joseph Gergaud
et al.
Abstract:In this article, based on two case studies, we discuss the role of abnormal geodesics in planar Zermelo navigation problems. Such curves are limit curves of the accessibility set, in the domain where the current is strong. The problem is set in the frame of geometric time optimal control, where the control is the heading angle of the ship and in this context, abnormal curves are shown to separate time minimal curves from time maximal curves and are both small-time minimizing and maximizing. We describe the sma… Show more
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