5.3.1. nvector.rotation.E_rotation

E_rotation(axes='e')

Returns rotation matrix R_Ee defining the axes of the coordinate frame E.

Parameters

axes‘e’ or ‘E’

defines orientation of the axes of the coordinate frame E. If axes is ‘e’ then z-axis points to the North Pole along the Earth’s rotation axis, x-axis points towards the point where latitude = longitude = 0. If axes is ‘E’ then x-axis points to the North Pole along the Earth’s rotation axis, y-axis points towards longitude +90deg (east) and latitude = 0.

Returns

R_Ee3 x 3 array

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

Notes

R_Ee controls the axes of the coordinate frame E (Earth-Centred, Earth-Fixed, ECEF) used by the other functions in this library. It is very common in many fields to choose axes equal to ‘e’, which is also the default in this library. Previously the old matlab toolbox the default value was equal to ‘E’. If you choose axes equal to ‘E’ 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.

References

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

Examples

>>> import numpy as np
>>> import nvector as nv
>>> np.allclose(nv.E_rotation(axes='e'), [[ 0,  0,  1],
...                                       [ 0,  1,  0],
...                                       [-1,  0,  0]])
True
>>> np.allclose(nv.E_rotation(axes='E'), [[ 1.,  0.,  0.],
...                                       [ 0.,  1.,  0.],
...                                       [ 0.,  0.,  1.]])
True