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A systematic approach for solving the great circle track problems based on vector algebra

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Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
Strony
3--13
Opis fizyczny
Bibliogr. 19 poz., rys., tab.
Twórcy
autor
  • Merchant Marine Department National Taiwan Ocean University 2 Pei-Ning Road, Keelung, 20224 TAIWAN
Bibliografia
  • 1. Bennett, G. G.: Practical Rhumb Line Calculations on the Spheroid. The Journal of Navigation, 49(1), pp. 112-119, 1996.
  • 2. Bowditch, N.: American Practical Navigator. Volume 2, DMAH/TC, Washington, 1981.
  • 3. Bowditch, N.: The American Practical Navigator. 2002 Bicentennial Edition, National Imagery and Mapping Agency, Maryland, 2002.
  • 4. Chen, C. L.: New Computational Approaches for Solving the Great Circle Sailing and Astronomical Vessel Position. Ph.D. Dissertation, Department of Civil Engineering, National Taiwan University, Taipei, Taiwan, 2003.
  • 5. Chen, C. L., Hsieh, T. H. and Hsu, T. P.: A Novel Approach to Solve the Great Circle Sailings Based on Rotation Transformation. Journal of Marine Science and Technology, 23(1), pp 13-20, 2015.
  • 6. Chen, C. L., Hsu, T. P., and Chang, J. R.: A Novel Approach to Great Circle Sailings: The Great Circle Equation. The Journal of Navigation, 57(2), pp. 311-320, 2004.
  • 7. Chen, C. L., Liu, P. F. and Gong, W. T.: A Simple Approach to Great Circle Sailing: The COFI Method. The Journal of Navigation, 67(3), pp. 403-418, 2014.
  • 8. Clough-Smith, J. H.: An Introduction to Spherical Trigonometry. Brown, Son & Ferguson, Ltd., Glasgow, 1966.
  • 9. Cutler, T. J.: Dutton’s Nautical Navigation. Fifteenth Edition, Naval Institute Press, Maryland, 2004.
  • 10. Earle, M. A., Sphere to Spheroid Comparison. The Journal of Navigation, 59(3), pp. 491-496, 2006.
  • 11. Greenberg, M. D.: Advanced Engineering Mathematics. Second Edition, Prentice-Hall International, Inc., 1998.
  • 12. Holm, R. J.: Great Circle Waypoints for Inertial Equipped Aircraft. NAVIGATION, Journal of the Institute of Navigation, 19(2), pp. 191-194, 1972.
  • 13. Jofeh, M. L.: The Analysis of Great-circle Tracks. The Journal of Navigation, 34(1), pp. 148-149, 1981.
  • 14. Keys, G.: Practical Navigation by Calculator. Stanford Maritime, London, 1983.
  • 15. Miller, A. R., Moskowitz, I. S. and Simmen, J.: Traveling on the Curved Earth. NAVIGATION, Journal of the Institute of Navigation, 38(1), pp. 71-78, 1991.
  • 16. Nastro, V. and Tancredi, U.: Great Circle Navigation with Vectorial Methods. The Journal of Navigation, 63(3), pp. 557-563, 2010.
  • 17. National Imagery and Mapping Agency (NIMA): Department of Defense World Geodetic System 1984: Its definition and relationship with local geodetic systems. Third Edition, Technical Report NIMA TR8350.2, 2000.
  • 18. Royal Navy: Admiralty Manual of Navigation: The Principles of Navigation, Volume 1. 10th Edition. The Nautical Institute, London, 2008.
  • 19. Spiegel, M. R., Lipschutz, S. and Spellman, D.: Vector analysis and an introduction to Tensor analysis. Second Edition, McGraw-Hill, 2009.
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-33653273-ff84-4a2e-a874-1be2fa8ac650
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