The static and dynamic properties of an asymmetric rigid body are studied using a Lagrangian approach. The body consists of a thin-walled cylinder balanced by a point mass attached to its inner surface. When resting on an inclined plane, stable and unstable equilibrium points are found, and oscillations about the stable point are studied for different angles of inclination and different values of the balancing mass. The analysis illustrates the utility of Lagrangian mechanics, and the derived results can be experimentally verified using simple materials.

中文翻译：

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平衡空心圆柱在斜面上的摆动

使用拉格朗日方法研究非对称刚体的静态和动态特性。主体由一个薄壁圆柱体组成，由附着在其内表面上的点质量平衡。当静止在倾斜平面上时，找到稳定和不稳定的平衡点，并研究了不同倾角和不同平衡质量值下围绕稳定点的振荡。分析说明了拉格朗日力学的效用，并且可以使用简单的材料通过实验验证得出的结果。