A note on time-optimal paths on perturbed spheroid

Abstract

We consider the Zermelo navigation problem on the ellipsoid of revolution (spheroid) in the presence of a perturbation $W$ determined by a mild velocity vector field, $|W|<1$, with application of Finsler metric of Randers type in the context of the corresponding optimal control represented by a time-efficient ship's heading $\phi (t)$ (steering direction). As the example we present the solutions to the problem on an oblate ellipsoid with acting infinitesimal rotation.

16 pages, 20 figures

References in corpus (1)

• Solution to the quantum Zermelo navigation problem

Cited by in corpus (3)

• Generalized Zermelo navigation on Hermitian manifolds under mild wind
• Application of planar Randers geodesics with river-type perturbation in search models
• On generalization of Zermelo navigation problem on Riemannian manifolds