Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica (Dec 2017)

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

  • Kopacz Piotr

DOI
https://doi.org/10.1515/auom-2017-0039
Journal volume & issue
Vol. 25, no. 3
pp. 107 – 123

Abstract

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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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