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 Killing–Cartan metrics of the rotation group.
Keywords: Rotation group as Riemannian space, Euler angles, Killing–Cartan metric, rigid body rotation, geodesic principle.
UDC: 531.37, 514.82
PACS: 04.50.Kd, 02.20.Hj
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. 18–27.