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.

这项工作涉及围绕主轴的对称刚体的动力学运动。假设物体有一个球形的腔，里面充满了粘性液体，还有一个可移动的质量，该质量与双弹性连接，点位于动态对称轴上，施加粘性摩擦。该物体受到回旋力矩的作用，其中前两个分量选择为零，第三个分量不为零。研究了粘性液体和可移动质量对建议运动的综合影响。所得结果表明，在存在内部耗散的情况下，当时间趋于无穷大时，系统的运动趋向于绕最大惯性矩轴的稳定旋转。绘制获得的结果以检测身体参数对运动的良好影响。控制系统的数值结果是应用四阶龙格-库塔方法获得的，并在其他图中表示。这项工作的意义在于在潜艇和陀螺仪行业领域的巨大应用。