On Generalised Single-Heading Navigation
| Autor: | Piotr Kopacz, Nicoleta Aldea |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
0209 industrial biotechnology
Current (mathematics) Spacetime 010102 general mathematics Mathematical analysis Perturbation (astronomy) Ocean Engineering 02 engineering and technology Oceanography 01 natural sciences Action (physics) 020901 industrial engineering & automation Dimension (vector space) Vector field 0101 mathematics Mathematics |
| Zdroj: | Journal of Navigation. 74:60-78 |
| ISSN: | 1469-7785 0373-4633 |
| DOI: | 10.1017/s0373463320000351 |
| Popis: | Introducing the notion of a pseudoloxodrome, we generalise a single-heading navigation to conformally flat Riemannian manifolds, under the action of a perturbing vector field (wind, current) of arbitrary force. The findings are applied to time-optimal navigation with the use of the Euler–Lagrange equations. We refer to the Zermelo navigation problem admitting space and time dependence of both a perturbation and a ship's speed. The necessary conditions for single-heading time-optimal navigation are obtained and the pseudoloxodromes of minimum and maximum time are discussed. Furthermore, we describe winds which yield the pseudoloxodromic and loxodromic time extremals. Our research is also illustrated with the examples in dimension two emphasising the single-heading solutions among the time-optimal trajectories in the presence of some space-dependent winds. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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