The slope-of-a-mountain problem in a cross gravitational wind

Time geodesics on a slippery slope under gravitational wind

“…The very recent results [1,3] have been encouraging enough to merit further investigation. Continuing the above line of research naturally led us to the new model of a slippery cross slope presented below.…”

“…In turn, the remaining part of gravitational wind, which is included in the equations of motion on the slippery slope, we call an active wind (denoted by G η in the slippery slope model). We can rewrite (1)…”

“…wind together with the minimum (zeroed) cross wind, for each direction of motion and gravity force ||G T || h , determines the classical Matsumoto's slope-of-a-mountain problem. On the other hand, the reversed setting yields the cross slope problem ( [1]) recalled right below. For clarity's sake, we also mention that a vector sum of the strongest effective wind and strongest cross wind gives full gravitational wind, so G η = G T , as is in ZNP.…”

“…Cross slope A different approach to time-optimal navigation on a mountain slope has been presented in [1] very recently (CROSS for short). Namely, unlike Matsumoto and for comparison to his standard set-up, the transverse component of gravitational wind was taken into account entirely in the equations of motion, whereas the along-gravity effect was reduced completely (see Figure 2, where CROSS is presented as a particular and edge case in further investigation).…”

“…Thus, it is reasonable to consider a reversed scenario, including the full cross-gravity effect and vanishing the entire along-gravity additive, which stands for the dead wind in this case. Recall from [1] that the slope model under the action of only cross-gravity impact has been called a cross slope. The solution is given by another Finsler metric of general (α, β)-type, i.e.…”