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

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.

Keywords

• zermelo navigation
• kropina metric
• riemann-finsler manifold
• timeminimal path
• perturbation
• 53b20
• 53c21
• 53c22
• 53c60
• 49j15
• 49j53