Approximate solution of the equations of motion of dynamically asymmetric body with a viscosity liquid

A mathematical model of the motion of a solid body of arbitrary shape with a spherical cavity relative to a fixed point is studied. The cavity is entirely filled with a fluid of high viscosity. The dynamic equations of motion are constructed by the method proposed by F. L. Chernousko, based on the application of the theorem on the change of kinetic momentum. The equations of motion are transformed taking into account the small dynamic asymmetry of the solid body. It is assumed that the small parameters characterising large viscosity and small asymmetry are of the same order. For the described case, numerical and approximate analytical dependences of the components of the angular velocity of a solid body in the associated reference frame on time by the Poincaré method are obtained, and the corresponding graphs are plotted. The accuracy of the approximate solutions has been evaluated, as well as the influence of the value of a small parameter on the error. Approximate analytical dependences allow us to study the influence of system parameters on the dynamics of motion. Practical application can be the use of the obtained results in the study of the motion of spacecraft with liquid propellant reserve on board.