In this paper, the motion of a rigid body in a singular case of the natural frequency () is considered. This case of singularity appears in the previous works due to the existence of the term in the denominator of the obtained solutions. For this reason, we solve the problem from the beginning. We assume that the body rotates about its fixed point in a Newtonian force field and construct the equations of the motion for this case when . We use a new procedure for solving this problem from the beginning using a large parameter that depends on a sufficiently small angular velocity component . Applying this procedure, we derive the periodic solutions of the problem and investigate the geometric interpretation of motion. The obtained analytical solutions graphically are presented using programmed data. Using the fourth-order Runge-Kutta method, we find the numerical solutions for this case aimed at determining the errors between both obtained solutions.

中文翻译：

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大参数技术在刚体奇异情况求解中的应用

在本文中，刚体在固有频率的奇异情况下的运动（）。由于存在术语“奇异性”，因此在以前的作品中出现过这种情况。在获得的解决方案的分母中。因此，我们从一开始就解决了问题。我们假设物体在牛顿力场中绕其固定点旋转，并针对这种情况构造运动方程。。我们从一开始就使用一个新的程序来解决此问题，该程序使用依赖于足够小的角速度分量的大参数。应用此程序，我们得出问题的周期解，并研究运动的几何解释。使用编程数据以图形方式显示获得的分析解决方案。使用四阶Runge-Kutta方法，我们找到了这种情况下的数值解，旨在确定两个获得的解之间的误差。