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Please use this identifier to cite or link to this item: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/41543

Title: A Systematic Approach for Solving the Great Circle Track Problems Based on Vector Algebra
Authors: Chih-Li Chen
Contributors: 國立臺灣海洋大學:商船學系
Keywords: spherical trigonometry
great circle
vector algebra
multiple products
Date: 2016-06
Issue Date: 2017-03-01T06:46:01Z
Publisher: Polish Maritime Research
Abstract: Abstract: A systematic approach, based on multiple products of the vector algebra (S-VA), is proposed to derive the spherical triangle formulae for solving the great circle track (GCT) problems. Because the mathematical properties of the geometry and algebra are both embedded in the S-VA approach, derivations of the spherical triangle formulae become more understandable and more straightforward as compared with those approaches which use the complex linear combination of a vector basis. In addition, the S-VA approach can handle all given initial conditions for solving the GCT problems simpler, clearer and avoid redundant formulae existing in the conventional approaches. With the technique of transforming the Earth coordinates system of latitudes and longitudes into the Cartesian one and adopting the relative longitude concept, the concise governing equations of the S-VA approach can be easily and directly derived. Owing to the advantage of the S-VA approach, it makes the practical navigator quickly adjust to solve the GCT problems. Based on the S-VA approach, a program namely GCTPro_VA is developed for friendly use of the navigator. Several validation examples are provided to show the S-VA approach is simple and versatile to solve the GCT problems.
Relation: 23(2)
URI: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/41543
Appears in Collections:[商船學系] 期刊論文

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