rotations may be extrinsic (rotations about the axes of the original coordinate system, which is assumed to remain motionless), or intrinsic (rotations about the axes of the rotating coordinate system , solidary with the moving body, which changes its orientation with respect to the extrinsic frame after each elemental rotation).

In the sections below, an axis designation with a prime mark superscript (e.g., ) denotes the new axis after an elemental rotation.

Euler angles are typically denoted as , or , respectively. Different

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