导航问题; $λ-$Funk 公设; 芬斯勒公设

arXiv - MATH - Differential Geometry Pub Date : 2024-09-18 DOI:arxiv-2409.12058

Newton Solórzano, Víctor León, Alexandre Henrique, Marcelo Souza

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引用次数: 0

摘要

我们从几何角度研究了导航问题中的旅行时间。该问题涉及欧几里得平面的一个开放子集，它代表了一个受到与离原点距离成正比的对称风流扰动的湖泊。从这个物理问题推导出的兰德斯度量概括了众所周知的笛卡尔平面上的欧几里得度量和单位圆盘上的丰度度量。我们得到了点到点、点到线、反之亦然的距离或旅行时间公式

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Navigation problem; $λ-$Funk metric; Finsler metric

We investigate the travel time in a navigation problem from a geometric perspective. The setting involves an open subset of the Euclidean plane, representing a lake perturbed by a symmetric wind flow proportional to the distance from the origin. The Randers metric derived from this physical problem generalizes the well-known Euclidean metric on the Cartesian plane and the Funk metric on the unit disk. We obtain formulas for distances, or travel times, from point to point, from point to line, and vice-versa

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arXiv - MATH - Differential Geometry

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