5.3.1. nvector.rotation.E_rotation¶
-
E_rotation
(axes='e')[source]¶ 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’. 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