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Great Circles and Rhumb Lines on the Complex Plane

Published online by Cambridge University Press:  25 January 2017

Robin G. Stuart
Robin G. Stuart*
Affiliation:
(Valhalla, New York, USA)
*
(E-mail: robinstuart@earthlink.net)
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Abstract

Mapping points on the Riemann sphere to points on the plane of complex numbers by stereographic projection has been shown to offer a number of advantages when applied to problems in navigation traditionally handled using spherical trigonometry. Here it is shown that the same approach can be used for problems involving great circles and/or rhumb lines and it results in simple, compact expressions suitable for efficient computer evaluation. Worked numerical examples are given and the values obtained are compared to standard references.

Keywords

AlgorithmNautical NavigationPath

Information

Type
Research Article
Information
The Journal of Navigation , Volume 70 , Issue 3 , May 2017 , pp. 618 - 627
Copyright
Copyright © The Royal Institute of Navigation 2017 

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References

REFERENCES

Arfken, G.B. and Weber, H.J. (1995). Mathematical Methods for Physicists, Academic Press.Google Scholar
Bowditch, N. (2002). The American Practical Navigator: An Epitome of Navigation, The National Imagery and Mapping Agency.Google Scholar
Donnay, J.D.H. (1945). Spherical Trigonometry after the Cesàro Method, Interscience Publishers, Inc., New York.Google Scholar
Earle, M.A. (2005). A Comment on Navigation Instruction, The Journal of Navigation, 58, 337–340.Google Scholar
Heard, W.B. (2006). Rigid Body Mechanics, Wiley-VCH Verlag, Weinheim.Google Scholar
Nevanlinna, R. and Paatero, V. (1969). Introduction to Complex Analysis, Reading Massachusetts.Google Scholar
Stuart, R.G. (1984). Applications of Complex Analysis to Spherical Coordinate Geometry, Quarterly Journal of the Royal Astronomical Society 25, 126–136; http://articles.adsabs.harvard.edu/full/1984QJRAS..25..126S Google Scholar
Stuart, R.G. (2009a). Applications of Complex Analysis to Celestial Navigation, NAVIGATION: Journal of the Institute of Navigation, 56, 221–227.Google Scholar
Stuart, R.G. (2009b). Applications of complex analysis to precession, nutation and aberration, Monthly Notices of the Royal Astronomical Society, 400, 1366–1372.Google Scholar
Tseng, W.-K., A. Earle, M.A. and Guo, J.-L. (2012). Direct and Inverse Solutions with Geodetic Latitude in Terms of Longitude for Rhumb Line Sailing. The Journal of Navigation, 65, 549–559.Google Scholar
Williams, R. (1998). Geometry of Navigation, Horwood Publishing Ltd, Chichester, UK.Google Scholar