Rigid body rotation in relativistic approximation

Abstract

In this research, relativistic rotation of a rigid body, which is generated by metric properties of Riman space of general relativity, is studied. The main purpose of this investigation is to obtain Lagrange function for the relativistic rotation of a rigid body. In order to attain this aims the whole system of point masses mi, in which a certain set of point masses dmn forms an “absolutely rigid body” mn in such a way that the condition of a constant distance between any two point masses from the set of point masses dmn holds, was investigated. In this case, the body mn can rotate around its own center of mass with angular velocity |ω| ≥ 0. The remaining point masses mj from the set mi are point bodies, which do not rotate. Lagrange function for the relativistic rotation of a rigid body is deriving from Lagrange function of the non-rotation point of masses system in the postnewtonian approximation.