# p_EB_E2n_EB_E: Convert cartesian position vector in meters to n-vector In nvctr: The n-vector Approach to Geographical Position Calculations using an Ellipsoidal Model of Earth

## Description

The position of B (typically body) relative to E (typically Earth) is given as cartesian position vector p_EB_E, in meters ("ECEF-vector").

## Usage

 `1` ```p_EB_E2n_EB_E(p_EB_E, a = 6378137, f = 1/298.257223563) ```

## Arguments

 `p_EB_E` Cartesian position vector from E to B, decomposed in E (3x1 vector) (m) `a` Semi-major axis of the Earth ellipsoid (m, default [WGS-84] 6378137) `f` Flattening of the Earth ellipsoid (no unit, default [WGS-84] 1/298.257223563)

## Details

The function converts to n-vector, n_EB_E and its depth, z_EB.

The calculation is exact, taking the ellipticity of the Earth into account. It is also nonsingular as both n-vector and p-vector are nonsingular (except for the center of the Earth). The default ellipsoid model used is WGS-84, but other ellipsoids (or spheres) might be specified.

## Value

n-vector representation of position B, decomposed in E (3x1 vector) (no unit) and depth of system B relative to the ellipsoid (z_EB = -height)

## References

Kenneth Gade A Nonsingular Horizontal Position Representation. The Journal of Navigation, Volume 63, Issue 03, pp 395-417, July 2010.

`n_EB_E2p_EB_E`, `n_EA_E_and_p_AB_E2n_EB_E` and `n_EA_E_and_n_EB_E2p_AB_E`
 ```1 2``` ```p_EB_E <- 6371e3 * c(0.9, -1, 1.1) (n_EB_E <- p_EB_E2n_EB_E(p_EB_E)) ```