Geodesic
An action of the Klein 4-group on the angular velocity
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXV, Tome 528 (2023), pp. 47-53

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Expressing the angular velocity via Euler angles is a key step, linking kinematics with rigid body dynamics. Once the components of angular velocity are found in a rotating frame, they are (simultaneously) found in an inertial (non-rotating) frame. And once the components are found for successive intrinsic rotations, they are just as readily found for successive extrinsic rotations. The action of the Klein 4-group on the angular velocity, which we describe in this paper, provides further insight into the kinematic relations of rigid body motion, including the critical motion of Dzhanibekov flipping wingnut. 
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     title = {An action of the {Klein} 4-group on the angular velocity},
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S. Adlaj. An action of the Klein 4-group on the angular velocity. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXV, Tome 528 (2023), pp. 47-53. http://geodesic.mathdoc.fr/item/ZNSL_2023_528_a2/