Convert Euler-Rodrigues vector to rotation angles
function calculates the set of rotation angles,
R3, for a given
Euler-Rodrigues (also known as Rodrigues) vector,
rotation used in this function is a passive transformation between two coordinate
Determine rotation angles from vector,
r = [.1 .2 -.1]; [yaw, pitch, roll] = rod2angle(r)
yaw = -0.1651 pitch = 0.4074 roll = 0.1651
rod— Rodrigues vector
M-by-3 matrix containing M Rodrigues vector.
S— Rotation sequence
Rotation angles, in radians, from which to determine Rodrigues
vector. For the default rotation sequence,
the rotation angle order is:
R1 — z-axis rotation
R2 — y-axis rotation
R3 — x-axis rotation
R1— First rotation angles
M-by-1 array of first rotation angles, in radians.
R2— Second rotation angles
M-by-1 array of second rotation angles, in radians.
R3— Third rotation angles
M-by-1 array of third rotation angles, in radians.
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.