c4dynamics.rotmat.rotmat.quat2dcm

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c4dynamics.rotmat.rotmat.quat2dcm#

c4dynamics.rotmat.rotmat.quat2dcm(quat)[source]#

Returns a Body-from-Reference Direction Cosine Matrix (DCM) of an attitude quaternion.

For a scalar-first unit quaternion \(q = [q_w, q_x, q_y, q_z]\), the DCM is given by:

\[\begin{split}R = \begin{bmatrix} 1 - 2(q_y^2 + q_z^2) & 2(q_x q_y + q_w q_z) & 2(q_x q_z - q_w q_y) \\ 2(q_x q_y - q_w q_z) & 1 - 2(q_x^2 + q_z^2) & 2(q_y q_z + q_w q_x) \\ 2(q_x q_z + q_w q_y) & 2(q_y q_z - q_w q_x) & 1 - 2(q_x^2 + q_y^2) \end{bmatrix}\end{split}\]

The result is identical to dcm321 with the Euler angles of the same attitude. The quaternion is normalized before the conversion.

Parameters:

quat (array_like) – A quaternion \([q_w, q_x, q_y, q_z]\).

Returns:

out (numpy.ndarray) – A 3x3 DCM matrix used to rotate a vector to the body frame from a reference frame of coordinates.

Examples

>>> import c4dynamics as c4d
>>> q = c4d.rotmat.euler2quat(theta = 30 * c4d.d2r)
>>> c4d.rotmat.quat2dcm(q) @ [1, 0, 0]  
[0.866  0  0.5]
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