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

Piotr Kopacz

doi:10.1515/auom-2017-0039

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

Differential Geometry 2019-03-25 v1 Optimization and Control

Authors: Piotr Kopacz

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Abstract

We generalize the Zermelo navigation problem and its solution on Riemannian manifolds $(M, h)$ admitting a space dependence of a ship's speed $0<|u(x)|_h\leq1$ 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.

Keywords

Zermelo navigation problem Riemannian manifolds strong perturbation Finsler metric Kropina type space-dependent speed

Cite

@article{arxiv.1606.01036,
  title  = {A note on generalization of Zermelo navigation problem on Riemannian manifolds with strong perturbation},
  author = {Piotr Kopacz},
  journal= {arXiv preprint arXiv:1606.01036},
  year   = {2019}
}

Comments

11 pages, 4(x2) figures

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