THE ROTATION OF UNELASTIC EARTH

                           Churkin V.A.

     Institute of Theoretical Astronomy, St-Petersburg, Russia

     Nowadays the rheological condition of the Earth's interior is
known with great uncertainty. Therefore the influence of the rheo-
logical qualities of the Earth on its rotation must be taken  into
consideration in the most general analytic form. In  our  opinion,
linear integral operators are such analytical forms. In fact,  in-
tegral operators allow to account the most  important  quality  of
the unelastic mediums - the effect of the hysteresis loop or othe-
rwise the effect of the phase lag of the unelastic medium's  reac-
tion on the external force, which with necessity leads to the dis-
sipation of the mechanical energy. Besides, every integral  opera-
tor hides the rheological information in its nucleus. This  allows
to preserve the mentioned nucleus in the symbolic form when const-
ructing the theory of the unelastic Earth rotation,  and  only  on
the finishing stages to reveal its analytical structure, thus  fi-
xing the concrete rheological qualities.
     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 (preserving the nucleus of the integral  operator  in
the symbolic form) with respect to the Laplace-images of the  com-
ponents of the angular velocity. Inverse Laplace-transformation in
this work we make for two types of nucleus of the integral  opera-
tor - for the nucleus of the Dirak Delta-function  (which  corres-
ponds to the rheological model of the elastic Earth) and  for  the
nucleus of the exponential type. In the context of these two types
of nucleus of the integral operator the expressions for  free  and
forced nutation of the Earth were obtained.