Abstract
In this paper the author shows a procedure to settle the computation of very long geodesic lines on the ellipsoid without using the series expansion. The integration of elliptic integrals appearing in the procedure is numerically carried out by means of a mechanical quadrature-the method of Repeated Interval Halving.
The author also devises formulae for the numerical solution of the problem, in order to make the amount of significance error least and determine the kind of quadrant for the computation of inverse trigonometric function.
The anti-podal problem for the direct and inverse solution is rigorously solved by this method.
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References
R.H. RAPP: From a Lecture Note of “Advanced Geometric Geodesy”, Ohio State University, 1967.
E.L. STIEFEL:An Introduction to Numerical Mathematics, Academic Press, 1963, pp. 149–155, (English Translation).
S.D. CONTE:Elementary Numerical Analysis, McGraw-Hill Book Company, 1965, pp. 10–12.
F.R. HELMERT:Die Mathematischen und Physikalischen Theorien Der Höheren Geodäsie, Druck und Verlag von B. G. Teubner, 1880, (Reprinted in 1962), I Teil, pp. 212–290.
H.F. RAINSFORD:Long Geodesics on the Ellipsoid, Bulletin Geodesique, 37, 1955, pp. 12–21.
D.L. DIMITRY and T.H. MOTT Jr.:Introduction to Fortran IV Programming, Holt, Rinehart and Winston, 1966.
J.B. SCARBOROUGH:Numerical Mathematical Analysis, sixth edition, The John Hopkins Press, 1966, pp. 208–212.
H.F. RAINSFORD, et al.: 1957 Report Study Group No. 2,Long Lines-Trilateration Adjustment, International Association of Geodesy, Bulletin Geodesique, 48, Juin, 1958, pp. 2–8.
E.M. SÖDONO:A Rigorous Non-Iterative Procedure for Rapid Inverse Solution of Very Long Geodesics, ibid., pp. 13–25.
G.T. McCAW:Long Lines on the Earth, Empire Survey Review Vol. II, pp. 156–163, 346–352, 505–508.
JORDAN—EGGERT—KNEISSL:Handbuch Der Vermessungkunde, Band IV, 1959, pp. 1074–1075.
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Saito, T. The computation of long geodesics on the ellipsoid by non-series expanding procedure. Bull. Geodesique 98, 341–373 (1970). https://doi.org/10.1007/BF02522166
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DOI: https://doi.org/10.1007/BF02522166