Convert Euler-Rodrigues vector to direction cosine matrix
Determine the direction cosine matrix from the Euler-Rodrigues vector.
r = [.1 .2 -.1]; DCM = rod2dcm(r)
DCM = 0.9057 -0.1509 -0.3962 0.2264 0.9623 0.1509 0.3585 -0.2264 0.9057
R— Rodrigues vector
M-by-3 matrix containing M Rodrigues vectors.
dcm— Direction cosine matrix
3-by-3-by-M containing M direction cosine matrices.
An Euler-Rodrigues vector represents a rotation by integrating a direction cosine of a rotation axis with the tangent of half the rotation angle as follows:
are the Rodrigues parameters. Vector represents a unit vector around which the rotation is performed. Due to the tangent, the rotation vector is indeterminate when the rotation angle equals ±pi radians or ±180 deg. Values can be negative or positive.
 Dai, J.S. "Euler-Rodrigues formula variations, quaternion conjugation and intrinsic connections." Mechanism and Machine Theory, 92, 144-152. Elsevier, 2015.