Analytical solution of the dynamic equations of motion of a solid body with a high viscosity liquid

The motion of a solid body with a spherical cavity filled with a high viscosity liquid is considered relative to a fixed point. To construct dynamic equations of motion, the method proposed by F.L. Chernousko, based on the application of the theorem on the change in angular momentum. For the case of a dynamically symmetric solid body, the first integral of motion is derived, exact analytical dependences of the components of the angular velocity of the solid body in a coupled reference frame on time are obtained, and the corresponding graphs are plotted. The obtained analytical dependencies allow us to study the influence of system parameters, including fluid, on the dynamics of its motion relative to a fixed point. Practical application can be the use of the results obtained in the study of the motion of spacecraft with a supply of liquid fuel on board.