The rotation matrix `R_AB`

is created based on 3 angles `x`

, `y`

and `z`

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

`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, codeT 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.

## Arguments

- x
Angle of rotation about new x axis (rad)

- y
Angle of rotation about new y axis (rad)

- z
Angle of rotation about new z axis (rad)

## Value

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

## References

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