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

Kopacz, Piotr

doi:10.1515/auom-2017-0039

Abstract

We generalize the Zermelo navigation on Riemannian manifolds (M; h), admitting a space dependence of a ship's speed 0 < |u(x)|_h ≤ 1 in the presence of a perturbation W̃ determined by a strong (critical) velocity vector field satisfying |W̃ (x)|_h = |u(x)|_h, with application of Finsler metric of Kropina type.

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

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