Differential Equation of the Loxodrome on a Helicoidal Surface

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JOURNAL OF NAVIGATION, vol.68, no.5, pp.962-970, 2015 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 68 Issue: 5
  • Publication Date: 2015
  • Doi Number: 10.1017/s0373463315000181
  • Title of Journal : JOURNAL OF NAVIGATION
  • Page Numbers: pp.962-970


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.