5.3.8. nvector.rotation.xyz2R¶

xyz2R(x, y, z)[source]¶

Returns rotation matrix from 3 angles about new axes in the xyz-order.

Parameters

x,y,z: real scalars or array of lengths n: Angles [rad] of rotation about new axes.

Returns

R_AB: 3 x 3 x n 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 = mdot(R_AB, v_B)

See also

R2xyz, zyx2R, R2zyx

Notes

The rotation matrix R_AB is created based on 3 angles x,y,z about new axes (intrinsic) in the order x-y-z. The 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 x about its x-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 z about its NEWEST z-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.