xyz2R {nvctr}

Create a rotation matrix from 3 angles about new axes in the xyz order.

Description

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:

1. 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).

2. Secondly, T is rotated an angle y about the NEW y-axis of T.

3. 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.

Usage

xyz2R(x, y, z)

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.

See Also

R2xyz, zyx2R and R2zyx.

Examples

xyz2R(rad(10), rad(20), rad(30))