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.

See also

zyx2R, xyz2R, R2xyz

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.