均质滑块沿粗糙球面滑动问题的动力学解析

Dynamic Analysis of the Problem of A Homogeneous Block Sliding on A Rough Spherical Surface

建立了均质滑块在粗糙球面上滑动问题的力学模型以及动力学方程,详细阐述了该动力学方程的推导求解过程,并绘制了滑块无量纲速度V随角度θ的变化曲线,将动力学方程的解析解形象地表述出来.通过V-θ曲线验证了均质滑块在粗糙球面上会出现减速停住、先减速后加速脱离、先减速停住后加速脱离等多种结果.在此基础上,还验证了均质滑块不能从粗糙球面顶点滑动到赤道位置的推论.

The mechanical model and dynamic equations of the sliding problem of a homogeneous sliding block on a rough spherical surface are established,the derivations and solution process of the dynamic equations are described in detail,and the curves of the change of the non-dimensional speed of the sliding block with the angle are drawn,and the analytical solution of the dynamic equation is vividly expressed.Through the V-θcurves,it is verified that the homogeneous sliding block will have many results on the rough sphere,such as slowing down and stopping,slowing down first and then accelerating and separating,and slowing down and stopping first and then accelerating and separating.On this basis,the inference that the homogeneous slider cannot slide from the vertex of the rough sphere to the equator position is also verified.