Geometry of a Navigation problem: The $\lambda-$Funk Finsler Metrics
Differential Geometry
2024-11-05 v2
Abstract
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
Cite
@article{arxiv.2409.12058,
title = {Geometry of a Navigation problem: The $\lambda-$Funk Finsler Metrics},
author = {Newton Solórzano and Víctor León and Alexandre Henrique and Marcelo Souza},
journal= {arXiv preprint arXiv:2409.12058},
year = {2024}
}