Numerical theory of rotation of the deformable Earth with the fluid core, and its fitting to VLBI data . ... Improved differential equations of the rotation of the deformable Earth with the two-layer fluid core are developed. ... Poincare's method of modeling the dynamical effects of the fluid core, and Sasao's approach for calculating the tidal interaction between the core and mantle in terms of the dynamical Love number are generalized for the case of the two-layer fluid core. ...