# Find the three angles about new axes in the zyx order from a rotation matrix

Source:`R/R2zyx.R`

`R2zyx.Rd`

The 3 angles `z`

, `y`

, `x`

about new axes (intrinsic) in the order z-y-x are
found from the rotation matrix `R_AB`

. The angles (called Euler angles or
Tait–Bryan angles) 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.

## Arguments

- R_AB
a 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

## Details

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.

## References

Kenneth Gade A Nonsingular Horizontal Position Representation.
*The Journal of Navigation*, Volume 63, Issue 03, pp 395-417, July 2010.