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The computation of long geodesics on the ellipsoid by non-series expanding procedure
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.
The computation of long geodesics on the ellipsoid by non-series expanding procedure
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.
The computation of long geodesics on the ellipsoid by non-series expanding procedure
Saito, Tsutomu (author)
1970
Article (Journal)
Electronic Resource
English
Geodäsie , Geometrie , Geodynamik , Mathematik , Mineralogie
Long geodesics on the ellipsoid
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The computation of long geodesics on the ellipsoid through Gaussian quadrature
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The Use of Bessel-Spheres for Solution of Problems Related to Geodesics on the Ellipsoid
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A rigorous non-iterative procedure for rapid inverse solution of very long geodesics
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