In this paper, the problem of the motion of a rigid body about a fixed point under the action of a Newtonian force field is studied when the natural frequency . This case of singularity appears in the previous works and deals with different bodies which are classified according to the moments of inertia. Using the large parameter method, the periodic solutions for the equations of motion of this problem are obtained in terms of a large parameter, which will be defined later. The geometric interpretation of the considered motion will be given in terms of Euler’s angles. The numerical solutions for the system of equations of motion are obtained by one of the well-known numerical methods. The comparison between the obtained numerical solutions and analytical ones is carried out to show the errors between them and to prove the accuracy of both used techniques. In the end, we obtain the case of the regular precession type as a special case. The stability of the motion is considered by the phase diagram procedures.

中文翻译：

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估计固有频率的刚体旋转运动的新处理

本文研究了自然频率下牛顿力场作用下刚体绕定点运动的问题。 。这种奇异的情况出现在以前的著作中，涉及根据惯性矩分类的不同物体。使用大参数方法，可以根据大参数获得该问题的运动方程的周期解，稍后将对其进行定义。所考虑运动的几何解释将以欧拉角给出。运动方程组的数值解是通过一种众所周知的数值方法获得的。将所得数值解与解析解进行比较，以显示它们之间的误差并证明这两种技术的准确性。最后，我们获得常规进动类型的情况作为特例。