Differential Equation of the Loxodrome on a Rotational Surface

Serdjo Kos, Renato Filjar, Mirano Hess

Abstract:	The loxodrome is a curve fairly often used in marine surface navigation primarily because it does not require a change of course. On the Mercator projection (standard marine nautical chart) the loxodrome is shown as a straight line, on the Earth conceived as a sphere it has the form of a spiral curve, while on the Earth shaped as a rotational elipsoid it takes the form of an irregular curve. In this paper the rotational surface (S) is given by parametrisation and the differential equation of the loxodrome on the rotational surface (S) determined in this way is derived by the application of differential geometry thereby defining at the same time the metric of such rotational surface (S), what is very convenient for use in marine applications.
Published in:	Proceedings of the 2009 International Technical Meeting of The Institute of Navigation January 26 - 28, 2009 Disney's Paradise Pier Hotel Anaheim, CA
Pages:	958 - 960
Cite this article:	Kos, Serdjo, Filjar, Renato, Hess, Mirano, "Differential Equation of the Loxodrome on a Rotational Surface," Proceedings of the 2009 International Technical Meeting of The Institute of Navigation, Anaheim, CA, January 2009, pp. 958-960.
Full Paper:	ION Members/Non-Members: 1 Download Credit Sign In