Frequency characteristic of a uniformly rotating laser gyro in exact and polynomial forms

In some inertial navigation systems of a carousel type, laser gyros operate in regime of uniform rotation. For development of such systems and computer simulation of their work, one needs to have the “exact” (in wide range of angular velocities ) analytical expression for counterpropagating waves beat frequency  of  uniformly rotating device. This expression may be obtained by solving the well-known system of laser gyro dynamic equations with accuracy to second order in parameters of counterpropagating waves linear coupling. But before use of such non-dithered laser gyros in the named inertial system, their metrological parameters (scale factors and null shifts) must be preliminary calibrated. For synthesis and qualitative analysis of methodical errors of the procedure of such calibration on a quickly rotating platform of a single-axis stand, one needs also to have the approximate analytical expression for counterpropagating waves beat frequency in the form of polynomial 
with coefficients , ...,   which involve parameters of the exact expression for . As analysis of the literature shows, the known expression for  and the known relations for some of coefficients of polynomial  are not complete and, therefore, must be modified. In the paper, the result of such modification is presented.