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Convert direction cosine matrix to rotation angles

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.

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