Maths - Rotations - Order of rotation operations

The rotation operation is not commutative.

In other words the order of Successive Rotations is significant, for example

This gives 90 degree rotation about Z axis,

whereas

This gives 90 degree rotation about y axis (first 2 lines cancel out)

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see also:	polar co-ordinates matrix algebra kinematics orientation rotations dynamics Conversion Euler To Matrix Conversion Euler to Quaternion Conversion Matrix to Euler Conversion Matrix to Quaternion Conversion Quaternion to Euler Conversion Quaternion to Matrix
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