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

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.