Abstract
In this paper, the Matsumoto slope-of-a-mountain problem is revisited. We present a general model of the slope as a Riemannian manifold, exploiting the influences of both transverse and longitudinal components of the gravitational wind on time-optimal paths. In contrast to the original Matsumoto’s exposition, the cross-gravity additive is taken into account in the equations of motion, while the along-gravity effect is entirely compensated. The purely geometric solutions to the problem are investigated by means of Finsler geometry. Our study explores the properties of the new cross-slope metric obtained in this work, which belongs to the class of general (α,β)-metrics, emphasizing the strong convexity conditions as well as the corresponding time geodesics. Using some relevant examples the developed theory is illustrated, while explaining and comparing the deformations of the Finslerian indicatrices and the behavior of time-minimal paths on the mountain slopes with different approaches to the gravity effect.
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