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2020, no. 2

ON PRINCIPLE OF GEODESICS IN THE SPACE OF THE LORENTZ GROUP PARAMETERS

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

In a previous paper, the authors substantiated the property of a body rotating relative to a fixed center of mass to realize the principle of geodesics with respect to the KillingCartan metric of this group in the space of parameters of the rotation group. In the present paper, the relativistic invariance of this property of a rotating body is proved, namely, a theorem is proved that the inertial motion of a rotating rigid body in the space of parameters of the rotation group as a subgroup of the Lorentz group corresponds to a curve that is geodesic in the internal space of the parameters of this group.

Keywords: Lorentz group, space of parameters of the rotation group as the Lorentz subgroup, rotating rigid body inertial motion, geodesic principle in the space of parameters.

UDC: 531.37, 514.82

PACS: 04.50.Kd, 02.20.Hj

DOI: 10.17238/issn2226-8812.2020.2.4-13

Please cite this article in English as:
Babourova O.V., Portnov Yu.A., Frolov B.N., Shamrova V.E. On principle of geodesics in the space of the Lorentz group parameters. Space, Time and Fundamental Interactions, 2020, no. 2, pp. 4-13.