A note on generalization of Zermelo navigation problem on Riemannian manifolds with strong perturbation

Abstract

We generalize the Zermelo navigation problem and its solution on Riemannian manifolds $(M,h)$ admitting a space dependence of a ship's speed $0<|u(x){|}_h\le 1$ in the presence of a perturbation $\tilde{W}$ determined by a strong velocity vector field satisfying $|\tilde{W}(x){|}_h=|u(x){|}_h$, with application of Finsler metric of Kropina type.

11 pages, 4(x2) figures

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• Solution to the quantum Zermelo navigation problem
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Cited by in corpus (1)

• Application of planar Randers geodesics with river-type perturbation in search models