On generalization of Zermelo navigation problem on Riemannian manifolds

DOI10.1142/S0219887819500580zbMath1425.53020arXiv1604.06487OpenAlexW2963978024WikidataQ115245332 ScholiaQ115245332MaRDI QIDQ5232414

Piotr Kopacz

Publication date: 3 September 2019

Published in: International Journal of Geometric Methods in Modern Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.06487

zbMATH Keywords

conformalZermelo navigationtime-minimal pathRanders-Kropina metricRiemann-Finsler manifold

Mathematics Subject Classification ID

Set-valued and variational analysis (49J53) Existence theories for optimal control problems involving ordinary differential equations (49J15) Geodesics in global differential geometry (53C22) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Global differential geometry of Finsler spaces and generalizations (areal metrics) (53C60) Local Riemannian geometry (53B20) Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing (76B10)

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Classification of time-optimal paths under an external force based on Jacobi stability in Finsler space ⋮ Zermelo deformation of Hermitian metrics by holomorphic vector fields ⋮ Unnamed Item ⋮ Generalized loxodromes with application to time-optimal navigation in arbitrary wind ⋮ Time-extremal navigation in arbitrary winds on conformally flat Riemannian manifolds

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