Brachystochronen als zeitkürzeste Fahrspuren von Bobschlitten

Abstract

Bobsled move on tracks with a known geometry, i.e. with a given cross-sectional shape, turn angle, and elevation drop. The problem is to find the time-shortest path through a turn. To investigate this problem the classical brachistochrone problem is generalized to arbitrarily twofold curved surfaces in the 3-dimensional Euclidean space. The corresponding equation of a minimum time path involves two other special extremals: the geodesics and the Jacobi geodesics.