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2018, no. 2

On geodesic in the space of the group rotation parameters

Babouriva O.V., Portnov Yu.A., Frolov B.N., Shamrova V.E.

It is proved that the geodesic principle for the free rotation of a rigid body is realized in the parameter space of the rotation group. Namely, it is shown that a free rotation of a rigid body corresponds, in the Riemannian space of the rotation group parameters, to a curve, which is a geodesic relative to the KillingCartan metrics of the rotation group.

Keywords: Rotation group as Riemannian space, Euler angles, KillingCartan metric, rigid body rotation, geodesic principle.

UDC: 531.37, 514.82

PACS: 04.50.Kd, 02.20.Hj

DOI: 10.17238/issn2226-8812.2018.2.18-27

Please cite this article in English as:
Babouriva O.V., Portnov Yu.A., Frolov B.N., Shamrova V.E. On geodesic in the space of the group rotation parameters. Space, Time and Fundamental Interactions, 2018, no. 2, pp. 1827.