MG11 
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On deriving Lagrange function in the problem of two rotary bodies with the method of symmetrization

At the present time in the problem of motion of bodies in GR, despite great efforts applied t to eliminate the discrepancies between the relativistic equations of body motion, obtained by different authors from Einstein’s field equation on the basis of various (sometimes even with the same) methods, there is still necessity in simpler approach of obtaining equation of motion without any difficult procedures of deriving these equations from the equation of field. In the present paper one of such possible methods is discussed. In fact, we use as a starting point the corrected metrics of the first approximation of Fock for a rotating liquid sphere [1,2] Unlike other similar metrics of the first approximation, in the metrics (1) the members nonlinear with respect to eigen momentum are taken into account. Then, it is easy to write LaGrange function of a probe body in the field of rotating liquid sphere. Appling the procedure of symmetrization, we find the members of LaGrange function resulting from the proper rotation of the probe body. The cross members are found by means of undetermined coefficients method. 1. M.M. Abdil’din. Bodies motion problem in General Relativity. Almaty, 2006. - 152 p. 2. M.M. Abdil’din Einstein’s mechanics of gravitation theory. Alma-Ata. 1988. - 198 p.