Aerospace Blockset™

Direction Cosine Matrix to Quaternions - Convert direction cosine matrix to quaternion vector

Library

Utilities/Axes Transformations

Description

The Direction Cosine Matrix to Quaternions block transforms a 3-by-3 direction cosine matrix (DCM) into a four-element unit quaternion vector (q₀,q₁,q₂,q₃). The DCM performs the coordinate transformation of a vector in inertial axes to a vector in body axes.

The DCM is defined as a function of a unit quaternion vector by the following:

Using this representation of the DCM, there is a number of calculations to arrive at the correct quaternion. The first of these is to calculate the trace of the DCM to determine which algorithms are used. If the trace is greater that zero, the quaternion can be automatically calculated. When the trace is less than or equal to zero, the major diagonal element of the DCM with the greatest value must be identified to determine the final algorithm used to calculate the quaternion. Once the major diagonal element is identified, the quaternion is calculated. For a detailed view of these algorithms, look under the mask of this block.

Dialog Box

Inputs and Outputs

See Also

Direction Cosine Matrix to Rotation Angles

Rotation Angles to Direction Cosine Matrix

Rotation Angles to Quaternions

Quaternions to Direction Cosine Matrix

Quaternions to Rotation Angles

Direction Cosine Matrix ECEF to NED to Latitude and Longitude

Direction Cosine Matrix to Rotation Angles