The geometry on the slope of a mountain

Time geodesics on a slippery slope under gravitational wind

“…because r i = r = r 0 = 0 under this assumption. Therefore, the ODE system (6) which yields the time-minimizing trajectories γ(t) = (γ i (t)), i = 1, ..., n on the slippery cross slope under the influence of the active wind G η is provided by the system (9), where the spray coefficients are Gi η (γ(t), γ(t)) from ( 46), with Fη (γ(t), γ(t)) = 1.…”

“…Since ||G T || h = ḡ/ √ 5 for the inclined plane z = x/2, while ||G T || h < 0.5 in the cross slope case (η = 1) 9. The limaçons simplify to the ellipses in the cases of Zermelo and Riemannian.…”