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Determine rotation vector from quaternion

The Quaternions to Rotation Angles block converts the
four-element quaternion vector (*q*_{0}, *q*_{1}, *q*_{2}, *q*_{3})
into the rotation described by the three rotation angles (R1, R2,
R3). The block generates the conversion by comparing elements in
the direction cosine matrix (DCM) as a function of the rotation angles.
The elements in the DCM are functions of a unit quaternion vector.
For example, for the rotation order * z-y-x*,
the DCM is defined as:

The DCM defined by a unit quaternion vector is:

From the preceding equation, you can derive the following relationships between DCM elements and individual rotation angles for a ZYX rotation order:

where Ψ is R1, Θ is R2, and Φ is R3.

Input | Dimension Type | Description |
---|---|---|

First | 4-by-1 quaternion vector | Contains the quaternion vector. |

Output | Dimension Type | Description |
---|---|---|

First | 3-by-3 vector | Contains the rotation angles, in radians. |

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.

The limitations for the `'ZYZ'`, `'ZXZ'`, `'YXY'`, `'YZY'`, `'XYX'`,
and `'XZX'` implementations generate an R2 angle
that is between 0 and 180 degrees, and R1 and R3 angles that are between
±180 degrees.

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