On generalization of Zermelo navigation problem on Riemannian manifolds

Abstract

We generalize the Zermelo navigation problem and its solution on Riemannian manifolds $(M,h)$ admitting a space dependence of a ship's own speed $|u(x){|}_h\le 1$ in the presence of a perturbation $W$ determined by a mild velocity vector field $|W(x){|}_h<|u(x){|}_h$, with application of Finsler metric of Randers type.

10 pages, 4 figures

References in corpus (4)

• Solution to the quantum Zermelo navigation problem
• Generalized Zermelo navigation on Hermitian manifolds under mild wind
• Application of planar Randers geodesics with river-type perturbation in search models
• A note on time-optimal paths on perturbed spheroid

Cited by in corpus (2)

• Finslerian geometrization of quantum mechanics in the hydrodynamical representation
• Time geodesics on a slippery cross slope under gravitational wind