Create a rotation matrix from 3 angles about new axes in the xyz order.Source:
The rotation matrix
R_AB is created based on 3 angles
about new axes (intrinsic) in the order x-y-z.
The angles (called Euler angles or Tait-Bryan angles) are defined by the following
procedure of successive rotations:
Given two arbitrary coordinate frames
B, consider a temporary frame
Tthat initially coincides with
A. In order to make
B, we first rotate
xabout its x-axis (common axis for both
Tis rotated an angle
yabout the NEW y-axis of
Finally, codeT is rotated an angle
zabout its NEWEST z-axis. The final orientation of
Tnow coincides with the orientation of
The signs of the angles are given by the directions of the axes and the right hand rule.
Angle of rotation about new x axis (rad)
Angle of rotation about new y axis (rad)
Angle of rotation about new z axis (rad)
3x3 rotation matrix (direction cosine matrix) such that the relation between a vector v decomposed in A and B is given by: v_A = R_AB * v_B
Kenneth Gade A Nonsingular Horizontal Position Representation. The Journal of Navigation, Volume 63, Issue 03, pp 395-417, July 2010.