Description Usage Arguments Details Value References See Also Examples

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.

1 | ```
R2zyx(R_AB)
``` |

`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 |

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.

z,y,x angles of rotation about new axes (rad)

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

1 |

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