A note on time-optimal paths on perturbed spheroid

DOI10.3934/jgm.2018005zbMath1405.53061arXiv1602.00167OpenAlexW2256917361WikidataQ129741461 ScholiaQ129741461MaRDI QIDQ1711940

Piotr Kopacz

Publication date: 18 January 2019

Published in: Journal of Geometric Mechanics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1602.00167

zbMATH Keywords

navigationrotationellipsoidFinsler geometryspheroidRanders metrictime-minimal pathZermelo problem

Mathematics Subject Classification ID

Applications of optimal control and differential games (49N90) Existence theories for optimal control problems involving ordinary differential equations (49J15) Geodesics in global differential geometry (53C22) Global differential geometry of Finsler spaces and generalizations (areal metrics) (53C60)

Related Items (6)

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 ⋮ On generalization of Zermelo navigation problem on Riemannian manifolds

Cites Work

• A Riemannian approach to Randers geodesics
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• Kropina metrics and Zermelo navigation on Riemannian manifolds
• Zermelo navigation on Riemannian manifolds
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• Application of codimension one foliation in Zermelo's problem on Riemannian manifolds
• Generalized Zermelo navigation on Hermitian manifolds under mild wind
• Sopra un problema di navigazione di Zermelo
• Time-optimal navigation through quantum wind
• Geodesics in Randers spaces of constant curvature
• Elementary Differential Geometry
• ERGODIC PERTURBATIONS OF DEGENERATE INTEGRABLE HAMILTONIAN SYSTEMS
• Über das Navigationsproblem bei ruhender oder veränderlicher Windverteilung
• Finsler Metrics with K = 0 and S = 0
• Elementary solution to the time-independent quantum navigation problem
• Geometry of the Katok examples
• Zermelo navigation in the quantum brachistochrone
• A note on generalization of Zermelo navigation problem on Riemannian manifolds with strong perturbation
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