Aerospace Blockset™

Rotation Angles to Direction Cosine Matrix

Rotation Angles to Quaternions - Calculate quaternion from rotation angles

Library

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). A quaternion vector represents a rotation about a unit vector ( ) through an 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.

Dialog Box

Rotation Order: Specifies the output rotation order for three wind rotation angles. From the list, select ZYX, ZYZ, ZXY, ZXZ, YXZ, YXY, YZX, YZY, XYZ, XYX, XZY, or XZX. The default is ZYX.

Inputs and Outputs

Input	Dimension Type	Description
First	3-by-1 vector	Contains the rotation angles, in radians.

Output	Dimension Type	Description
First	4-by-1 matrix	Contains the quaternion vector.

Assumptions and Limitations

The limitations for the 'ZYX', 'ZXY', 'YXZ', 'YZX', 'XYZ', and 'XZY' implementations generate an R2 angle that is between +/-90 degrees, and R1 and R3 angles that are between +/-180 degrees.