Asymptotic analysis and numerical solutions for the rigid body containing a viscous liquid in cavity in the presence of gyrostatic moment

This work touches upon the dynamical motion of a symmetric rigid body around a principal axis. It is assumed that the body has a cavity of spherical form filled with a viscous liquid and a movable mass connected with double elastically with a point lying on the axis of dynamical symmetry that exerts a viscous friction. This body is acted upon by a gyrostatic moment, in which the first two components are selected to be null and the third one is different from zero. The combined effect of both the viscous liquid and the movable mass on the suggested motion is studied. The achieved results reveal that in the existence of internal dissipation, the motion of the system approaches to a steady rotation around the axis of greatest inertia moment when time tends to infinity. The attained results are plotted to detect the good impact of the body parameter on the motion. Numerical results of the governing system are obtained applying the fourth-order Runge-Kutta method and represented in other plots. The significance of this work is focused on the great applications in the field of submarines and gyroscopes industries.