Time geodesics on a slippery slope under gravitational wind
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.
scientific article; zbMATH DE number 7629233
scientific article