In this paper, the motion of a disk about a fixed point under the influence of a Newtonian force field and gravity one is considered. We modify the large parameter technique which is achieved by giving the body a sufficiently small angular velocity component about the fixed -axis of the disk. The periodic solutions of motion are obtained in the neighborhood tends to 0. This case of study is excluded from the previous works because of the appearance of a singular point in the denominator of the obtained solutions. Euler-Poison equations of motion are obtained with their first integrals. These equations are reduced to a quasilinear autonomous system of two degrees of freedom and one first integral. The periodic solutions for this system are obtained under the new initial conditions. Computerizing the obtained periodic solutions through a numerical technique for validation of results is done. Two types of analytical and numerical solutions in the new domain of the angular velocity are obtained. Geometric interpretations of motion are presented to show the orientation of the body at any instant of time .

中文翻译：

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应用大参数技术解决光盘绕固定点的缓慢旋转运动

在本文中，考虑了在牛顿力场和重力作用下圆盘绕固定点的运动。我们修改其通过使身体得到足够小的角速度分量实现大参数技术绕固定-轴盘的。在附近获得运动的周期解趋向于0。由于在获得的解的分母中出现奇异点，因此本研究案例不包括在以前的研究中。用它们的第一积分获得运动的欧拉-泊松方程。这些方程被简化为具有两个自由度和一个第一积分的拟线性自治系统。该系统的周期解是在新的初始条件下获得的。通过数值技术对获得的周期解进行计算机处理，以验证结果。在角速度的新域中获得了两种解析解和数值解。提出了运动的几何学解释，以显示身体在任何时刻的方向。