타원면에 대한 측지선
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측지학 |
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타원면[1]에 대한 측지선[2](geodesics on an ellipsoid, 타원체에 대한 곧은 선들) 연구는 특히 삼각측량 네트워크(triangulation network)의 솔루션과 관련하여 측지학과 관련하여 발생했다. 지구의 모양(figure of the Earth)은 약간 납작한 구인 편평 타원체로 잘 근사된다. 측지선은 평면 표면의 직선과 유사한 곡면의 두 지점 사이의 가장 짧은 경로이다. 따라서 타원면에 대한 삼각 측량 네트워크의 솔루션은 구면 삼각법의 연습 문제 세트이다 (Euler 1755) .
회전 타원체 상의 측지선
[편집]삼축 타원체 상의 측지선
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[편집]참고 문헌
[편집]- Arnold, V. I. (1989). 《Mathematical Methods of Classical Mechanics》. 번역 Vogtmann, K.; Weinstein, A. 2판. Springer-Verlag. ISBN 978-0-387-96890-2. OCLC 4037141.
- Bagratuni, G. V. (1967) [1962]. 《Course in Spheroidal Geodesy》. doi:10.5281/zenodo.32371. OCLC 6150611. Translation from Russian of Курс сфероидической геодезии (Moscow, 1962) by U.S. Air Force (FTD-MT-64-390)
- Berger, M. (2010). 《Geometry Revealed》. 번역 Senechal, L. J. Springer. doi:10.1007/978-3-540-70997-8. ISBN 978-3-540-70996-1.
- Bessel, F. W. (2010) [1825]. 번역 Karney, C. F. F.; Deakin, R. E.. “The calculation of longitude and latitude from geodesic measurements”. 《Astronomische Nachrichten》 331 (8): 852–861. arXiv:0908.1824. Bibcode:2010AN....331..852K. doi:10.1002/asna.201011352. S2CID 118760590. English translation of Astron. Nachr. 4, 241–254 (1825). Errata.
- Bliss, G. A. (1916). “Jacobi's condition for problems of the calculus of variations in parametric form”. 《Transactions of the American Mathematical Society》 17 (2): 195–206. doi:10.1090/S0002-9947-1916-1501037-4.
- Bomford, G. (1952). 《Geodesy》. Oxford: Clarendon. OCLC 1396190.
- Borre, K.; Strang, W. G. (2012). 〈11, Geometry of the Ellipsoid〉 (PDF). 《Algorithms for Global Positioning》. Wellesley-Cambridge Press. ISBN 978-0-9802327-3-8. OCLC 795014501.
- Cayley, A. (1870). “On the geodesic lines on an oblate spheroid”. 《Philosophical Magazine》. 4th series 40 (268): 329–340. doi:10.1080/14786447008640411.
- Chasles, M. (1846). “Sur les lignes géodésiques et les lignes de courbure des surfaces du second degré” [Geodesic lines and the lines of curvature of the surfaces of the second degree]. 《Journal de Mathématiques Pures et Appliquées》 (프랑스어) 11: 5–20. PDF.
- Christoffel, E. B. (1869). “Allgemeine Theorie der geodätischen Dreiecke” [General theory of geodesic triangles]. 《Abhandlungen Königlichen Akademie der Wissenschaft zu Berlin》 (독일어): 119–176.
- Clairaut, A. C. (1735). “Détermination géometrique de la perpendiculaire à la méridienne tracée par M. Cassini” [Geometrical determination of the perpendicular to the meridian drawn by Jacques Cassini]. 《Mémoires de l'Académie Royale des Sciences de Paris 1733》 (프랑스어): 406–416.
- Danielsen, J. S. (1989). “The Area under the Geodesic”. 《Survey Review》 30 (232): 61–66. doi:10.1179/003962689791474267.
- Darboux, J. G. (1894). 《Leçons sur la théorie générale des surfaces》 [Lessons on the general theory of surfaces] (프랑스어) 3. Paris: Gauthier-Villars. OCLC 8566228.
- Dupin, P. C. F. (1813). 《Développements de Géométrie》 [Developments in geometry] (프랑스어). Paris: Courcier. OCLC 560800801.
- Ehlert, D. (1993). 《Methoden der ellipsoidischen Dreiecksberechnung》 [Methods for ellipsoidal triangulation] (기술 보고서). Reihe B: Angewandte Geodäsie, Heft Nr. 292 (독일어). Deutsche Geodätische Kommission. OCLC 257615376.
- Euler, L. (1755). “Élémens de la trigonométrie sphéroïdique tirés de la méthode des plus grands et plus petits” [Elements of spheroidal trigonometry taken from the method of maxima and minima]. 《Mémoires de l'Académie Royale des Sciences de Berlin 1753》 (프랑스어) 9: 258–293. Figures.
- FAI (2018). 〈Section 8.2.3〉. 《FAI Sporting Code》 (PDF) (기술 보고서). Lausanne, Switzerland: Fédération Aéronautique Internationale.
- Forsyth, A. R. (1927). 《Calculus of Variations》. Cambridge Univ. Press. ISBN 978-1-107-64083-2. OCLC 250050479.
- Gan'shin, V. V. (1969) [1967]. 《Geometry of the Earth Ellipsoid》. 번역 Willis, J. M. St. Louis: Aeronautical Chart and Information Center. doi:10.5281/zenodo.32854. OCLC 493553. Translation from Russian of Геометрия земного эллипсоида (Moscow, 1967).
- Gauss, C. F. (1902) [1828]. 《General Investigations of Curved Surfaces of 1827 and 1825》. 번역 Morehead, J. C.; Hiltebeitel, A. M. Princeton Univ. Lib. OCLC 7824448. PDF. English translation of Disquisitiones generales circa superficies curvas (Dieterich, Göttingen, 1828).
- Hart, A. S. (1849). “Geometrical demonstration of some properties of geodesic lines”. 《Cambridge and Dublin Mathematical Journal》 4: 80–84.
- Helmert, F. R. (1964) [1880]. 《Mathematical and Physical Theories of Higher Geodesy》 1. St. Louis: Aeronautical Chart and Information Center. doi:10.5281/zenodo.32050. OCLC 17273288. English translation of Die Mathematischen und Physikalischen Theorieen der Höheren Geodäsie, Vol. 1 (Teubner, Leipzig, 1880).
- Hilbert, D.; Cohn-Vossen, S. (1952). 《Geometry and the Imagination》. 번역 Nemenyi, P. New York: Chelsea. ISBN 9780828400879. OCLC 301610346.
- Hutton, C. (1811). 《A Course of Mathematics in Three Volumes Composed for the Use of the Royal Military Academy》 3. London: F. C. and J. Rivington. OCLC 18031510.
- Jacobi, C. G. J. (1837). “Zur Theorie der Variations-Rechnung und der Differential-Gleichungen” [The theory of the calculus of variations and of differential equations]. 《Journal für die Reine und Angewandte Mathematik》 (독일어) 1837 (17): 68–82. doi:10.1515/crll.1837.17.68. S2CID 119469290.
- Jacobi, C. G. J. (1839). “Note von der geodätischen Linie auf einem Ellipsoid und den verschiedenen Anwendungen einer merkwürdigen analytischen Substitution” [The geodesic on an ellipsoid and various applications of a remarkable analytical substitution]. 《Journal für die Reine und Angewandte Mathematik》 (독일어) 1839 (19): 309–313. doi:10.1515/crll.1839.19.309. S2CID 121670851. Letter to Bessel, Dec. 28, 1838. French translation (1841).
- Jacobi, C. G. J. (2009) [1866]. A. Clebsch, 편집. 《Lectures on Dynamics》. 번역 Balagangadharan, K. New Delhi: Hindustan Book Agency. ISBN 978-81-85931-91-3. MR 2569315. OCLC 440645889. English translation of Vorlesungen über Dynamik (Reimer, Berlin, 1866). Errata.
- Jacobi, C. G. J. (1891). 〈Über die Curve, welche alle von einem Punkte ausgehenden geodätischen Linien eines Rotationsellipsoides berührt〉 [The envelope of geodesic lines emanating from a single point on an ellipsoid]. K. T. W. Weierstrass. 《Jacobi's Gesammelte Werke》 (독일어) 7. Berlin: Reimer. 72–87쪽. OCLC 630416023. Op. post., completed by F. H. A. Wangerin. PDF.
- Jekeli, C. (2012), 《Geometric Reference Systems in Geodesy》, Ohio State Univ., hdl:1811/51274
- Jordan, W.; Eggert, O. (1962) [1941]. 《Handbook of Geodesy》 3. 번역 Carta, M. W. Washington, DC: Army Map Service. Bibcode:1962hage.book.....J. doi:10.5281/zenodo.35316. OCLC 34429043. English translation of Handbuch der Vermessungskunde, 8th edition (Metzler, Stuttgart, 1941).
- Karney, C. F. F. (2013). “Algorithms for geodesics”. 《Journal of Geodesy》 87 (1): 43–55. arXiv:1109.4448. Bibcode:2013JGeod..87...43K. doi:10.1007/s00190-012-0578-z. Addenda.
- Karney, C. F. F. (2015). “GeographicLib”. Version 1.44.
- Karney, C. F. F. (2024). “Geodesics on an arbitrary ellipsoid of revolution”. 《Journal of Geodesy》 98 (1): 4:1–14. arXiv:2208.00492. doi:10.1007/s00190-023-01813-2.
- Klingenberg, W. P. A. (1982). 《Riemannian Geometry》. de Gruyer. ISBN 978-3-11-008673-7. MR 666697. OCLC 8476832.
- Knörrer, H. (1980). “Geodesics on the ellipsoid”. 《Inventiones Mathematicae》 59 (2): 119–143. Bibcode:1980InMat..59..119K. doi:10.1007/BF01390041. S2CID 118792545.
- Krakiwsky, E. J.; Thomson, D. B. (1974), 《Geodetic position computations》 (PDF), Dept. of Geodesy and Geomatics Engineering, Lecture Notes (39), Fredericton, N.B.: Univ. of New Brunswick, Bibcode:1974gpc..book.....K
- Laplace, P. S. (1829) [1799a]. 〈Book 1, §8.〉. 《Treatise on Celestial Mechanics》 1. 번역 Bowditch, N. Boston: Hillard, Gray, Little, & Wilkins. OCLC 1294937.
- Laplace, P. S. (1799b). 《Traité de Mécanique Céleste》 [Treatise on Celestial Mechanics] (프랑스어) 2. Paris: Crapelet. 112쪽. OCLC 25448952.
- Legendre, A. M. (1806). “Analyse des triangles tracées sur la surface d'un sphéroïde” [Analysis of spheroidal triangles]. 《Mémoires de l'Institut National de France》 (프랑스어) (1st semester): 130–161.
- Legendre, A. M. (1811). 《Exercices de Calcul Intégral sur Divers Ordres de Transcendantes et sur les Quadratures》 [Exercises in Integral Calculus] (프랑스어). Paris: Courcier. OCLC 312469983.
- Leick, A.; Rapoport, L.; Tatarnikov, D. (2015). 《GPS Satellite Surveying》 4판. Wiley. ISBN 978-1-119-01828-5.
- Liouville, J. (1846). “Sur quelques cas particuliers où les équations du mouvement d'un point matériel peuvent s'intégrer” [On special cases where the equations of motion of a point particle can be integrated]. 《Journal de Mathématiques Pures et Appliquées》 (프랑스어) 11: 345–378. PDF
- Lyusternik, L. (1964). 《Shortest Paths: Variational Problems》. Popular Lectures in Mathematics 13. 번역 Collins, P.; Brown, R. B. New York: Macmillan. MR 0178386. OCLC 1048605. Translation from Russian of Кратчайшие Линии: Вариационные Задачи (Moscow, 1955).
- Monge, G. (1850) [1796]. 〈Sur les lignes de courbure de la surface de l'ellipsoïde〉 [On the lines of curvature on the surface of the ellipsoid]. J. Liouville. 《Application de l'Analyse à la Géometrie》 (프랑스어) 5판. Paris: Bachelier. 139–160쪽. OCLC 2829112. (Fig. 1–2, Fig. 3–4). 1796 edition (Fig. 1–2, Fig. 3–4). PDF Figures.
- National Geodetic Survey (2012). “Geodesic Utilities: Inverse and Forward”. Version 3.0.
- Newton, I. (1848) [1687]. 〈Book 3, Proposition 19, Problem 3〉. 《The Mathematical Principles of Natural Philosophy》. 번역 Motte, A. New York: Adee. 405–409쪽. English translation of Philosophiæ Naturalis Principia Mathematica. Liber Tertius, Prop. XIX. Prob. II. pp. 422–424.
- Oriani, B. (1806). “Elementi di trigonometria sferoidica, Pt. 1” [Elements of spheroidal trigonometry]. 《Memorie dell'Istituto Nazionale Italiano》 (이탈리아어) 1 (1): 118–198.
- Oriani, B. (1808). “Elementi di trigonometria sferoidica, Pt. 2” [Elements of spheroidal trigonometry]. 《Memorie dell'Istituto Nazionale Italiano》 (이탈리아어) 2 (1): 1–58.
- Oriani, B. (1810). “Elementi di trigonometria sferoidica, Pt. 3” [Elements of spheroidal trigonometry]. 《Memorie dell'Istituto Nazionale Italiano》 (이탈리아어) 2 (2): 1–58.
- Poincaré, H. (1905). “Sur les lignes géodésiques des surfaces convexes” [Geodesics lines on convex surfaces]. 《Transactions of the American Mathematical Society》 (프랑스어) 6 (3): 237–274. doi:10.2307/1986219. JSTOR 1986219.
- Rainsford, H. F. (1955). “Long geodesics on the ellipsoid”. 《Bulletin Géodésique》 37 (1): 12–22. Bibcode:1955BGeod..29...12R. doi:10.1007/BF02527187. S2CID 122111614.
- Rapp, R. H. (1991), 《Geometric geodesy, part I》, Ohio State Univ., hdl:1811/24333
- Rapp, R. H. (1993), 《Geometric geodesy, part II》, Ohio State Univ., hdl:1811/24409
- RNAV (2007). 〈Appendix 2.〉. 《Order 8260.54A, The United States Standard for Area Navigation》 (PDF) (기술 보고서). Washington, D.C.: U.S. Federal Aviation Administration.
- Sjöberg, L. E. (2006). “Determination of areas on the plane, sphere and ellipsoid”. 《Survey Review》 38 (301): 583–593. doi:10.1179/003962606780732100.
- UNCLOS (2006). 《A Manual on Technical Aspects of the United Nations Convention on the Law of the Sea, 1982》 (PDF) (기술 보고서) 4판. Monaco: International Hydrographic Bureau. 2013년 5월 24일에 원본 문서 (PDF)에서 보존된 문서. 2013년 8월 15일에 확인함.
- Vincenty, T. (1975). “Direct and inverse solutions of geodesics on the ellipsoid with application of nested equations” (PDF). 《Survey Review》 23 (176): 88–93. Bibcode:1975SurRv..23...88V. doi:10.1179/sre.1975.23.176.88. Addendum: Survey Review 23 (180): 294 (1976).
- Vincenty, T.; Bowring, B. R. (1978). 《Application of three-dimensional geodesy to adjustments of horizontal networks》 (PDF) (기술 보고서). NOAA. NOS NGS-13.
- Weierstrass, K. T. W. (1861). “Über die geodätischen Linien auf dem dreiaxigen Ellipsoid” [Geodesic lines on a triaxial ellipsoid]. 《Monatsberichte der Königlichen Akademie der Wissenschaft zu Berlin》 (독일어): 986–997.