Time geodesics on a slippery slope under gravitational wind. (February 2023) - Aldea, Nicoleta; Kopacz, Piotr
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.