Differential Equation of the Loxodrome on a Helicoidal Surface
JOURNAL OF NAVIGATION, vol.68, no.5, pp.962-970, 2015 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 68 Issue: 5
- Publication Date: 2015
- Doi Number: 10.1017/s0373463315000181
- Journal Name: JOURNAL OF NAVIGATION
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.962-970
- Keywords: Loxodrome, Helicoidal Surface, Euclidean Space, MINKOWSKI 3-SPACE, SPACE
- Open Archive Collection: AVESIS Open Access Collection
- Yozgat Bozok University Affiliated: Yes
Abstract
In nature, science and engineering, we often come across helicoidal surfaces. A curve on a helicoidal surface in Euclidean 3-space is called a loxodrome if the curve intersects all meridians at a constant azimuth angle. Thus loxodromes are important in navigation. In this paper, we find the differential equation of the loxodrome on a helicoidal surface in Euclidean 3-space. Also we give some examples and draw the corresponding pictures via the Mathematica computer program to aid understanding of the mathematics of navigation.