archimedes.spatial.quaternion_to_dcm

archimedes.spatial.quaternion_to_dcm(quat: ndarray) → ndarray

Direction cosine matrix from unit quaternion

If the quaternion represents the attitude of a body B relative to a frame A, then this function returns the matrix R_BA that transforms vectors from frame A to frame B. Specifically, for a vector v_A expressed in frame A, the corresponding vector in frame B is given by v_B = R_BA @ v_A.

The inverse transformation can be obtained by transposing this matrix: R_AB = R_BA.T.

Note that this function assumes the scalar-first convention, and assumes the quaternion is normalized.

Parameters:

quat (array_like, shape (4,)) – Unit quaternion representing rotation from frame A to frame B, in the format [w, x, y, z] where w is the scalar part.

Returns:

Direction cosine matrix R_BA that transforms vectors from frame A to frame B.

Return type:

np.ndarray, shape (3, 3)