Читать книгу Global Navigation Satellite Systems, Inertial Navigation, and Integration - Mohinder S. Grewal - Страница 113

The radius of curvature of the reference ellipsoid surface in the east–west direction (i.e. orthogonal to the direction in which the meridional radius of curvature is measured) is called the transverse radius of curvature. It is the radius of the osculating circle in the local east–up plane, as illustrated in Figure 3.11, where the arrows at the point of tangency of the transverse osculating circle are in the local ENU coordinate directions. As this figure illustrates, on an oblate Earth, the plane of a transverse osculating circle does not pass through the center of the Earth, except when the point of osculation is at the equator. (All osculating circles at the poles are in meridional planes.) Also, unlike meridional osculating circles, transverse osculating circles generally lie outside the ellipsoidal surface, except at the point of tangency and at the equator, where the transverse osculating circle is the equator.

Figure 3.11 Transverse osculating circle.

The formula for the transverse radius of curvature on an ellipsoid of revolution is

(3.11)

where is the semimajor axis of the generating ellipse and is its eccentricity.