Institute of Theoretical Astronomy, St-Petersburg, Russia
In our work the initial well known algebraic equation, con- necting the angular velocity of the elastic body with its inertia moments, is replaced by the integral operator. On the base of this hypothesis the integro-differential equations of the Earth rotati- on, generalizing the differential equations of Eyler-Liuville, were obtained. Then, by using the Laplace-transformation the ini- tial system of integro-differential equations is solved in the general form of Duhamel`s integral. In terms of Eyler`s angles the real and imaginary parts of Duamel`s integral are respectively nu- tation and precession of free and non-free unelastic Earth.
We consider two types of nucleus of the integral operator - - the nucleus of the Dirak Delta-function (which corresponds to the rheological model of the elastic Earth) and the nucleus of the exponential type. In the context of these two types of nucleus the expressions for forced nutation and precession of the Earth were obtained.