Claessens, S.J. 2006

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  • p. 16

[math]tan θ = \frac{a}{b} tan β =\frac{a^2}{b^2} tan ϑ[/math] , где 

[math]\theta[/math] - co-latitude, geocentric,
[math]\vartheta[/math] - co-latitude, geodetic,
[math]\beta[/math] - co-latitude, reduced
  • p. 17

Claessens, S.J. 2006.png

Прямоугольная система координат#Z вверх, где 

[math]\nu[/math] - Радиус Земли, поперечный
[math]Q^\prime[/math] - Датум, точка на поверхности
  • p. 20

[math]\phi = \theta - \vartheta[/math], где [math]\phi[/math] - deflection angle, ellipsoidal

from spherical to ellipsoidal harmonics[edit]

  • p. ii

Numerical closed-loop simulations have shown that the accuracy of geopotential coefficients obtained with the new methods is significantly higher than the accuracy of existing methods that use the spherical harmonic framework.

  • p. 2

The error resulting from a spherical approximation is often assumed to be of the order of the flattening of the Earth (∼ 0.3%), but may be even larger due to the combined effect of subsequent approximations (e.g., Sans`o and Tscherning, 2003; Tscherning, 2004). For a geoid-ellipsoid separation of 100 m, the error induced by a spherical approximation is therefore in the order of 30 cm and possibly larger... aim to compute a geoid model accurate to 1 cm (Rapp, 1997a). Naturally, highly accurate modelling of the geoid and the Earth’s external gravity field is only possible if the required rigorous theoretical methodologies exist. This calls for a solution of a BVP where the boundary is formed by an ellipsoid of revolution, i.e., an ellipsoidal BVP.

  • p. 12

The ideal is to obtain a practical solution in the spherical harmonic framework that can match or even supersede the accuracy of the methods based on ellipsoidal harmonics.