Work

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

Year: 2025

Type: article

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 traveltime, from point to point, and the circumference equations. In addition, we obtain the distance formulas from point to line and vice versa.

Source: Ciência e Natura

DOI: 10.5902/2179460x88467

Authors: Newton Mayer Solórzano Chávez, Víctor Arturo Martínez León, Alexandre Henrique Rodrigues Filho, Marcelo Almeida de Souza

Institutions: Universidade Federal da Integração Latino-Americana, Universidade Federal de Goiás

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4408593083

FWCI:

Cites: 12

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Related to: 10