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On Generalised Single-Heading Navigation

Published online by Cambridge University Press:  10 July 2020

Nicoleta Aldea  and
Piotr Kopacz Open the ORCID record for Piotr Kopacz [Opens in a new window]
Nicoleta Aldea
Affiliation:
(Faculty of Mathematics and Computer Science, Transilvania University of Braşov, Braşov, Romania)
Piotr Kopacz*
Affiliation:
(Faculty of Navigation, Gdynia Maritime University, Gdynia, Poland)
*
(E-mail:p.kopacz@wn.umg.edu.pl)
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Abstract

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.

Keywords

Single-Heading NavigationPseudoloxodromeZermelo Navigation ProblemTime-Optimal Path

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Type
Research Article
Information
The Journal of Navigation , Volume 74 , Issue 1 , January 2021 , pp. 60 - 78
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Copyright
Copyright © The Royal Institute of Navigation 2020

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