Geometry of a navigation problem: the $\lambda-$Funk Finsler Metrics

Authors

DOI:

https://doi.org/10.5902/2179460X88467

Keywords:

Navigation problem, λ−Funk metric, Finsler metric

Abstract

We investigate the travel time in a navigation problem from a geometric perspective, with respect to a new class of Finsler metrics. We present the λ−Funk Finsler Metrics. The setting involves an open disk centered at the origin, representing a circular lake perturbed by a symmetric wind flow proportional to the distance from the origin with proportionality factor λ. The Randers metric, which is an important Finsler metric, derived from this physical problem, generalizes the well-known Euclidean metric (λ = 0) on the Cartesian plane and the Funk metric on the unit disk (λ = 1). We obtain the formula for distance, or travel
time, from point to point, and the circumference equations. In addition, we obtain the distance formulas from point to line and vice versa.

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Author Biographies

Newton Mayer Solórzano Chávez, Universidade Federal da Integração Latino-Americana

Doctor in Mathematics.

Víctor Arturo Martínez León, Universidade Federal da Integração Latino-Americana

Post-doctorate (2019) in Mathematics.

Alexandre Henrique Rodrigues Filho, Universidade Federal da Integração Latino-Americana

Studying Physical Engineering.

Marcelo Almeida de Souza, Universidade Federal de Goiás

Post-Doctorate in Mathematics from the University of Brasília.

References

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Published

2025-03-14

How to Cite

Chávez, N. M. S., León, V. A. M., Rodrigues Filho, A. H., & Souza, M. A. de. (2025). Geometry of a navigation problem: the $\lambda-$Funk Finsler Metrics. Ciência E Natura, 47, e88467. https://doi.org/10.5902/2179460X88467

Issue

Vol. 47 (2025): Publicação contínua

Section

Mathematics

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