<abstract xmlns="http://www.w3.org/1999/xhtml">We generalize the Zermelo navigation on Riemannian manifolds (M; h), admitting a space dependence of a ship's speed 0 &lt; |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. </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.

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

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

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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...

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

Published Online: Mar 31, 2018

Page range: 107 - 123

Received: Dec 23, 2016

Accepted: Jan 31, 2017

DOI: https://doi.org/10.1515/auom-2017-0039

Keywords
Zermelo navigation, Kropina metric, Riemann-Finsler manifold, timeminimal path, perturbation

© 2018

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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

Published Online: Mar 31, 2018

Page range: 107 - 123

Received: Dec 23, 2016

Accepted: Jan 31, 2017

DOI: https://doi.org/10.1515/auom-2017-0039

KeywordsZermelo navigation, Kropina metric, Riemann-Finsler manifold, timeminimal path, perturbation

© 2018

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Zermelo navigation, Kropina metric, Riemann-Finsler manifold, timeminimal path, perturbation