Convert direction cosine matrix to rotation angles

Utilities/Axes Transformations

The Direction Cosine Matrix to Rotation
Angles block converts a 3-by-3 direction cosine matrix (DCM) into
three rotation angles R1, R2, and R3, respectively the first, second,
and third rotation angles. The DCM matrix performs the coordinate
transformation of a vector in inertial axes into a vector in body
axes. The block **Rotation Order** parameter specifies
the order of the block output rotations. For example, if **Rotation
Order** has a value of `ZYX`

, the block
outputs are in the rotation order * z-y-x* (psi
theta phi).

**Rotation Order**Specifies the output rotation order for three rotation angles. From the list, select

`ZYX`

,`ZYZ`

,`ZXY`

,`ZXZ`

,`YXZ`

,`YXY`

,`YZX`

,`YZY`

,`XYZ`

,`XYX`

,`XZY`

, or`XZX`

. The default is`ZYX`

.**Limitation**The

`'Default'`

limitations for the`'ZYX'`

,`'ZXY'`

,`'YXZ'`

,`'YZX'`

,`'XYZ'`

, and`'XZY'`

implementations generate an`R2`

angle that lies between ±90 degrees, and`R1`

and`R3`

angles that lie between ±180 degrees.The

`'Default'`

limitations for the`'ZYZ'`

,`'ZXZ'`

,`'YXY'`

,`'YZY'`

,`'XYX'`

, and`'XZX'`

implementations generate an`R2`

angle that lies between 0 and 180 degrees, and`R1`

and`R3`

angles that lie between ±180 degrees.The

`'ZeroR3'`

limitations for the`'ZYX'`

,`'ZXY'`

,`'YXZ'`

,`'YZX'`

,`'XYZ'`

, and`'XZY'`

implementations generate an`R2`

angle that lies between ±90 degrees, and`R1`

and`R3`

angles that lie between ±180 degrees. However, when`R2`

is ±90 degrees,`R3`

is set to 0 degrees.The

`'ZeroR3'`

limitations for the`'ZYZ'`

,`'ZXZ'`

,`'YXY'`

,`'YZY'`

,`'XYX'`

, and`'XZX'`

implementations generate an`R2`

angle that lies between 0 and 180 degrees, and`R1`

and`R3`

angles that lie between ±180 degrees. However, when`R2`

is 0 or ±180 degrees,`R3`

is set to 0 degrees.

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

First | 3-by-3 matrix | Contains the direction cosine matrix. |

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

First | 3-by-1 vector | Contains the rotation angles, in radians. |

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