Generalized normal radius of curvature for correct computation of angular rate

The meridional (north-south or NS) and the normal (east-west or EW) radii of curvature on an ellipsoid are used with the level velocity components to compute the angular rates (of velocity) in the EW and NS directions. In other words, the velocity vector is decomposed first to compute the level angular rates along these principal directions. There is an alternative, one can start with the level velocity and the generalized normal radius of curvature to obtain the level angular velocity and then decompose this angular rate into its EW and NS components. Decomposition is thus accomplished from the angular velocity vector, not from the linear velocity vector. The term "generalized" is used to emphasize that the normal radius of curvature is NOT restricted to the two very special NS and EW normal directions. The purpose of this paper is to show the need to use the generalized normal radius of curvature on an ellipsoid in angular rate computation.