In this paper, we consider the problem of the rotational motion of a rigid body with an irrational value of the frequency . The equations of motion are derived and reduced to a quasilinear autonomous system. Such system is reduced to a generating one. We assume a large parameter proportional inversely with a sufficiently small component of the angular velocity which is assumed around the major or the minor axis of the ellipsoid of inertia. Then, the large parameter technique is used to construct the periodic solutions for such cases. The geometric interpretation of the motion is obtained to describe the orientation of the body in terms of Euler’s angles. Using the digital fourth-order Runge-Kutta method, we determine the digital solutions of the obtained system. The phase diagram procedure is applied to study the stability of the attained solutions. A comparison between the considered numerical and analytical solutions is introduced to show the validity of the presented techniques and solutions.

中文翻译：

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具有不合理固有频率的刚体的运动

在本文中，我们考虑具有频率无理值的刚体的旋转运动问题。运动方程被推导并简化为准线性自治系统。这样的系统被简化为发电系统。我们假设一个大参数与分量足够小成反比绕惯性椭圆的长轴或短轴假定的角速度的角。然后，使用大参数技术来构造这种情况的周期解。获得了运动的几何解释，以欧拉角来描述身体的方向。使用数字四阶Runge-Kutta方法，我们确定了所获得系统的数字解。相图程序用于研究所获得解决方案的稳定性。介绍了所考虑的数值和解析解决方案之间的比较，以证明所提出的技术和解决方案的有效性。