Here [B.sub.2] is

integration constant. In this case, using (17), the EoS parameter for Einstein-Aether gravity can be written as

where C is an

integration constant which will be determined by using reality condition of [square root of -G].

At tuning the current (torque) loop to the maximum speed, the influence of elastic mechanical oscillations on it for the

integration constant of the current loop [T.sub.T] << [T.sub.y] ([T.sub.y] = 1/[[OMEGA].sub.12]) and [gamma] = 1.01-1.5 is considered insignificant [7] which allows the transfer function to be adopted after conversion as [W.sub.KT] (p) [approximately equal to] 1.0.

In addition, substituting (2) into (9), the

integration constant [c.sub.1] was obtained as follows:

where [[rho].sub.0] is an

integration constant. In this case, (38) takes the form

where [[alpha].sub.2] = [[beta].sub.2], [[alpha].sub.1] = 1, [[beta].sub.1] = 1/t, and the

integration constant is zero.

Integrating (11) twice and assuming the

integration constant to be zero, we obtain

where C is an

integration constant. The

integration constant is constant in the tube since the tube is assumed to be symmetric.

Integrating (9) once and setting the

integration constant to zero, we obtain

Their amplitudes and phases are given by two complex

integration constants. Since, by definition, there should be no retrograde quasi-diurnal motion of the pole in either reference frames, we chose only one complex

integration constant (initial position of the pole) and constrain the other one so that the free diurnal motion disappears.