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The formulas of spherical triangle, which are widely used to solve various navigation problems, are the important basic knowledge of nautical mathematics. Because the sine rules and the cosine rules for the sides are the fundamental formulas to derive the other spherical triangle formulas, they are also called the genetic codes of the spherical triangle formulas. In the teaching process, teachers usually use the geometric method to derive and prove these fundamental formulas. However, the derivation of geometric methods is complicated and difficult to understand. To improve the teaching process, this paper proposes the three-dimensional rotation method, which is based on conversion of two cartesian coordinate frames using the rotation matrices. This method can easily and simultaneously derive the sine rules, the cosine rules for the sides, and the five-part formulas (I), and is also helpful to solve different kinds of spherical navigation problems.
Rocznik
Tom
Strony
553--558
Opis fizyczny
Bibliogr. 7 poz., rys.
Twórcy
autor
- Shanghai Maritime University, Shanghai, China
autor
- Shanghai Maritime University, Shanghai, China
autor
- Shanghai Maritime University, Shanghai, China
autor
- Shanghai Maritime University, Shanghai, China
autor
- National Taiwan Ocean University, Zhongzheng, Keelung, Taiwan
Bibliografia
- 1. Hsu T. P., Chen C. L., Chang J. R. (2005). New Computational Methods for Solving Problems of the Astronomical Vessel Position. The Journal of Navigation, 58(2): 315-335. - doi:10.1017/S0373463305003188
- 2. Clough-Smith J. H. (1966). An Introduction to Spherical Trigonometry. Brown, Son & Ferguson, Ltd.
- 3. Todhunter I. (1886). Spherical Trigonometry: For the Use of Colleges and Schools”, Fifth ed., Macmillan and Company.
- 4. Smart W. M. (1977). Text-Book on Spherical Astronomy, Sixth ed., Cambridge University Press.
- 5. Green R. M. (1985). Spherical Astronomy, Cambridge University Press.
- 6. Arfken G. (1985). Mathematical Methods for Physicists, Third ed., Academic Press.
- 7. Bowditch N. (1981). American Practical Navigator, Pub. 9, Vol. 2, Defense Mapping Agency Hydrographic/Topographic Center.
Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-5de02739-281f-48b1-bbfc-be54065eed39