论文标题
在革命的情况下，2D-Zermelo导航问题的异常大地学和小时球的粉丝形状
Abnormal Geodesics in 2D-Zermelo Navigation Problems in the Case of Revolution and the Fan Shape of the Small Time Balls
论文作者
论文摘要
在本文中，基于两个案例研究，我们讨论了异常的大地测量学在平面Zermelo导航问题中的作用。这样的曲线是在电流强的域中可访问性集的极限曲线。该问题设置在几何时间最佳控制框架中，其中控制是船的标题角，在这种情况下，异常曲线显示出可将时间最小曲线与时间最大曲线分开，并且都小时最小化和最大化。我们描述了小球。在更大的时间内，可以在异常方向上发生尖锐的奇异性，这对应于沿着非平滑图像的共轭点。它是根据时间最小值函数的规律性属性来解释的。
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 small-time minimal balls. For bigger time, a cusp singularity can occur in the abnormal direction, which corresponds to a conjugate point along the non-smooth image. It is interpreted in terms of the regularity property of the time minimal value function.
