Time geodesics on a slippery slope under gravitational wind
type: Item
instance of: scholarly article
title: Time geodesics on a slippery slope under gravitational wind
author: Nicoleta Aldea
author: Piotr Kopacz
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2022-12-08T00:00:00Z
review text: The authors of the paper introduced the concept of a slippery slope we generalize and interlink Matsumoto's slope-of-a-mountain problem with Zermelo's navigation problem on Riemannian manifolds under the influence of a weak gravitational wind. The purely geometric solutions for time-minimal navigation on a slippery slope are discussed by means of Finsler geometry. This includes the study of strong convexity conditions for the slippery slope metric, which belongs to the class of the general \((\alpha,\beta)\)-metrics and the related time geodesics, controlled by a traction coefficient. Several relevant examples demonstrate this new application of the developed theory, while explaining in particular the evolution of the indicatrices (time fronts) and behaviour of time-minimal paths on the slippery slopes, depending on the gravitational wind force and traction. The results obtained by the authors are very interesting in this field.
reviewed by: V. K. Chaubey
Mathematics Subject Classification ID: 53B40
Mathematics Subject Classification ID: 53C60
zbMATH DE Number: 7629233
zbMATH Keywords: time geodesic
zbMATH Keywords: Matsumoto metric
zbMATH Keywords: Zermelo navigation
zbMATH Keywords: Randers metric
zbMATH Keywords: Riemannian manifold
zbMATH Keywords: gradient vector field
MaRDI profile type: Publication
full work available at URL: j.na.2022.113160
OpenAlex ID: W4307898233
cites work: Q4661850
cites work: Zermelo navigation on Riemannian manifolds
cites work: Q5441364
cites work: Sprays metrizable by Finsler functions of constant flag curvature
cites work: Surfaces of revolution admitting strongly convex slope metrics
cites work: The geometry on the slope of a mountain
cites work: Q5705858
cites work: Zermelo deformation of Finsler metrics by Killing vector fields
cites work: Holonomy in the quantum navigation problem
cites work: On the definition and examples of Finsler metrics
cites work: Unexpected behaviour of flag and \(S\)-curvatures on the interpolated Poincaré metric
cites work: Projectively flat Matsumoto metric and its approximation
cites work: A Finsler geodesic spray paradigm for wildfire spread modelling
cites work: A slope of a mountain is a Finsler surface with respect to a time measure
cites work: Theory of Finsler spaces with \((\alpha,\beta)\)-metric
cites work: Geodesics in Randers spaces of constant curvature
cites work: Finsler Metrics with K = 0 and S = 0
cites work: Introduction to Matsumoto metric
cites work: Kropina metrics and Zermelo navigation on Riemannian manifolds
cites work: On a new class of Finsler metrics
cites work: Über das Navigationsproblem bei ruhender oder veränderlicher Windverteilung
cites work: On Einstein Matsumoto metrics
DOI: 10.1016/J.NA.2022.113160
description: scientific article; zbMATH DE number 7629233