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 
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/
@article{ZNSL_2023_528_a2,
     author = {S. Adlaj},
     title = {An action of the {Klein} 4-group on the angular velocity},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {47--53},
     year = {2023},
     volume = {528},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2023_528_a2/}
}
TY  - JOUR
AU  - S. Adlaj
TI  - An action of the Klein 4-group on the angular velocity
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2023
SP  - 47
EP  - 53
VL  - 528
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2023_528_a2/
LA  - en
ID  - ZNSL_2023_528_a2
ER  - 
%0 Journal Article
%A S. Adlaj
%T An action of the Klein 4-group on the angular velocity
%J Zapiski Nauchnykh Seminarov POMI
%D 2023
%P 47-53
%V 528
%U http://geodesic.mathdoc.fr/item/ZNSL_2023_528_a2/
%G en
%F ZNSL_2023_528_a2

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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.

[1] S. Adlaj, Torque free motion of a rigid body: from Feynman wobbling plate to Dzhanibekov flipping wingnut, https://semjonadlaj.com/SP/TFRBM.pdf

[2] S. Adlaj, “Galois axis”, International Scientific Conference “Infinite-Dimensional Analysis and Mathematical Physics” (Dedicated to the memory of Sergei Vasilyevich Fomin) (Moscow, Russsia, January 28–February 1, 2019), 9–11 https://semjonadlaj.com/Galois/GaloisAxis190129.pdf

[3] A. Seliverstov, “On circular sections of a second-order surface”, Computer tools in education, 2020, no. 4, 59–68 http://ipo.spb.ru/journal/index.php?article/2258/ | DOI

[4] N. E. Misyura, E. A. Mityushov, Kvaternionnye modeli v kinematike i dinamike tverdogo tela, Uralskii federalnyi universitet, Ekaterinburg, 2020, 120 pp.

[5] I. Bulyzhenkov, Vertexes in kinetic space-matter with local stresses instead of localized particles with distant gravitation | DOI