5.3.7. nvector.rotation.R2zyx¶
-
R2zyx
(R_AB)[source]¶ Returns the angles about new axes in the zxy-order from a rotation matrix.
- Parameters
- R_AB: 3x3 array
rotation matrix [no unit] (direction cosine matrix) such that the relation between a vector v decomposed in A and B is given by: v_A = np.dot(R_AB, v_B)
- Returns
- z, y, x: real scalars
Angles [rad] of rotation about new axes.
Notes
The z, x, y angles are called Euler angles or Tait-Bryan angles and are defined by the following procedure of successive rotations: Given two arbitrary coordinate frames A and B. Consider a temporary frame T that initially coincides with A. In order to make T align with B, we first rotate T an angle z about its z-axis (common axis for both A and T). Secondly, T is rotated an angle y about the NEW y-axis of T. Finally, T is rotated an angle x about its NEWEST x-axis. The final orientation of T now coincides with the orientation of B.
The signs of the angles are given by the directions of the axes and the right hand rule.
Note that if A is a north-east-down frame and B is a body frame, we have that z=yaw, y=pitch and x=roll.
See also: https://en.wikipedia.org/wiki/Aircraft_principal_axes https://en.wikipedia.org/wiki/Euler_angles https://en.wikipedia.org/wiki/Axes_conventions