This function returns the axes of the coordinate frame E (Earth-Centered, Earth-Fixed, ECEF).

## Usage

R_Ee(axes = "e")

## Arguments

axes

Either 'e' or 'E'

• 'e': z-axis points to the North Pole along the Earth's rotation axis, x-axis points towards the point where latitude = longitude = 0. This choice is very common in many fields.

• 'E': x-axis points to the North Pole along the Earth's rotation axis, y-axis points towards longitude +90deg (east) and latitude = 0. (the yz-plane coincides with the equatorial plane). This choice of axis ensures that at zero latitude and longitude, frame N (North-East-Down) has the same orientation as frame E. If roll/pitch/yaw are zero, also frame B (forward-starboard-down) has this orientation. In this manner, the axes of frame E is chosen to correspond with the axes of frame N and B. The functions in this library originally used this option.

## Value

rotation matrix defining the axes of the coordinate frame E as described in Table 2 in Gade (2010)

## Details

There are two choices of E-axes that are described in Table 2 in Gade (2010):

• e: z-axis points to the North Pole and x-axis points to the point where latitude = longitude = 0. This choice is very common in many fields.

• E: x-axis points to the North Pole, y-axis points towards longitude +90deg (east) and latitude = 0. This choice of axis directions ensures that at zero latitude and longitude, N (North-East-Down) has the same orientation as E. If roll/pitch/yaw are zero, also B (Body, forward, starboard, down) has this orientation. In this manner, the axes of E is chosen to correspond with the axes of N and B.

## References

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

## Examples

R_Ee()
#>      [,1] [,2] [,3]
#> [1,]    0    0    1
#> [2,]    0    1    0
#> [3,]   -1    0    0