V. I. Tsurkov ,   A. A. Gourchenkov International conference on optimization: techniques and application, UK University of Swansea , 06.1993 , language: английский  Аннотация The subject of the consideration is the motion of the viscous incompressible fluid in the cavity of rotating bodies. Experiments show that velocity fields have a thin boundary layer near by inside surfaces if the Ekman's number is great. The rest of fluid motion does not differ almost from this one of Ideal fluid. The normal velocity component of viscous fluid is equal approximately to this value of ideal fluid. The tangent velocity component changes fast in the boundary layer. The equations of the weakly disturbed body motion containing viscous fluid are introduced. The motion equations are linearized near by the uniform rotation. The influence of the fluid on the body motion is carried out by means of connection inertance coefficients which are determined by the Zhoukovski's potentials. These ones are the solution of the linear boundary eigen value problem which depend on the geometry of the cavity. The viscosity of the fluid is taken into account by means of generalized dissipative forces according to Landau's method. The body motion equations are the infinite Integral differential system. The first three equations describe the equivalent body motiton by inter moments of forces. The rest of ones determines fluid oscillations. The fluid velocity field is written as series. The coefficients of these ones are amplitudes of fluid oscillations. The integral differential system is solved by means of Landau's transformation. Afterwards the types of fluid oscillations are determined. We obtain the fluid velocity field and calculate the moment of viscous friction forces on the body. The stability problem of the free body containing viscous fluid is considered. The stability of the oscillations is analyzed by means of the disturbance theory. The generalized stability criterion is offered. Computational tests give the stability boundaries of the body with cylindrical cavity.  Ключевые слова viscous fluid, rotating body, stability