Convert rotation angles to Euler-Rodrigues vector
function converts the
rotation described by the three rotation angles,
R3, into an
M-by-3 Euler-Rodrigues matrix,
rotation used in this function is a passive transformation between two coordinate
converts the rotation described by the three rotation angles and a
rotation sequence, S, into an M-by-3 Euler-Rodrigues
rod, that contains the M Rodrigues
Determine the Rodrigues Vector from One Rotation Angle
Determine the Rodrigues vector from rotation angles.
yaw = 0.7854; pitch = 0.1; roll = 0; r = angle2rod(yaw,pitch,roll)
r = -0.0207 0.0500 0.4142
Determine Rodrigues Vectors from Multiple Rotation Angles
Determine the Rodrigues vectors from multiple rotation angles.
yaw = [0.7854 0.5]; pitch = [0.1 0.3]; roll = [0 0.1]; r = angle2rod(pitch,roll,yaw,'YXZ')
r = 0.0207 0.0500 0.4142 0.0885 0.1381 0.2473
R1 — First rotation angle
First rotation angle, in radians, from which to determine Euler-Rodrigues vector. Values must be real.
R2 — Second rotation angle
Second rotation angle, in radians, from which to determine Euler-Rodrigues vector. Values must be real.
R3 — Third rotation angle
Third rotation angle, in radians, from which to determine Euler-Rodrigues vector. Values must be real.
S — Rotation sequence
ZYX (default) |
Rotation sequence. For the default rotation sequence,
the rotation angle order is:
R1 — z-axis rotation
R2 — y-axis rotation
R3 — x-axis rotation
rod — Euler-Rodrigues vector
Euler-Rodrigues vector determined from rotation angles.
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.
Introduced in R2017a