Model of controlled snow lift and its hydrodynamic analogy

In this paper we formulate and investigate a problem of mountain-skier quickest controlled descent along a given surface. The main model assumption is that all potential energy change is compensated by sliding friction work. Analytical expressions of quickest controlled descent optimal trajectories are obtained for several classes of surfaces; in particular, it is shown that an optimal trajectory on revolving surface is a spiral. We represent here analytical and numerical results in the cases of free and fixed boundary points. Analogies between liquid discharge from a bleed hole and the model of mountain-skier controlled quickest descent are discussed in the conclusion.