Rotation Angles to Quaternions
Calculate quaternion from rotation angles
- Library:
Aerospace Blockset / Utilities / Axes Transformations
Description
The Rotation Angles to Quaternions block converts the rotation described by the three rotation angles (R1, R2, R3) into the four-element quaternion vector (q0, q1, q2, q3), where quaternion is defined using the scalar-first convention. Aerospace Blockset™ uses quaternions that are defined using the scalar-first convention. For more information on quaternions, see Algorithms.
Limitations
The limitations for the
ZYX,ZXY,YXZ,YZX,XYZ, andXZYimplementations generate an R2 angle that is between ±90 degrees, and R1 and R3 angles that are between ±180 degrees.The limitations for the
ZYZ,ZXZ,YXY,YZY,XYX, andXZXimplementations generate an R2 angle that is between 0 and 180 degrees, and R1 and R3 angles that are between ±180 degrees.
Ports
Input
Output
Parameters
Algorithms
A quaternion vector represents a rotation about a unit vector through the angle θ. A unit quaternion itself has unit magnitude, and can be written in the following vector format:
An alternative representation of a quaternion is as a complex number,
where, for the purposes of multiplication:
The benefit of representing the quaternion in this way is the ease with which the quaternion product can represent the resulting transformation after two or more rotations.
Extended Capabilities
See Also
Direction Cosine Matrix to Quaternions | Quaternions to Direction Cosine Matrix | Quaternions to Rotation Angles | Rotation Angles to Direction Cosine Matrix