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

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