Time geodesics on a slippery slope under gravitational wind. (February 2023)

• Record Type: Journal Article
• Authors: Aldea, Nicoleta; Kopacz, Piotr
• Is Part Of: Nonlinear analysis. Volume 227(2023)
• Publication Date: 2023-02
• Subjects: 53B40 -- 53C60; Time geodesic -- Matsumoto metric -- Zermelo navigation -- Randers metric -- Riemannian manifold -- Gradient vector field; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2022.113160
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: By introducing 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 ( α, β ) -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.