<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

A Systematic Approach for Solving the Great Circle Track Problems based on Vector Algebra

Polish Maritime Research

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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...

A Systematic Approach for Solving the Great Circle Track Problems based on Vector Algebra

Published Online: Jun 30, 2016

Page range: 3 - 13

DOI: https://doi.org/10.1515/pomr-2016-0014

Keywords
great circle, vector algebra, multiple products, spherical trigonometry

© 2016 Chih-Li Chen, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

A Systematic Approach for Solving the Great Circle Track Problems based on Vector Algebra

Published Online: Jun 30, 2016

Page range: 3 - 13

DOI: https://doi.org/10.1515/pomr-2016-0014

Keywordsgreat circle, vector algebra, multiple products, spherical trigonometry

© 2016 Chih-Li Chen, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
great circle, vector algebra, multiple products, spherical trigonometry