玻璃弹珠中的趣味动力学

MULTI-RIGID-BODY DYNAMICS SIMULATION WITH CONTACT AND FRICTION

  • 摘要: 用手去推倾斜的V形槽中排成一列的刚体小球,实验表明,小球的运动具有不稳定性,即初始球数为奇数时,第2个小球(从下向上数)会首先从V形槽中被挤出;而球数为偶数时,第3个小球会首先被挤出. 对于这种有趣的现象,考虑接触间存在库仑摩擦,进行了数值模拟,得到了与实验完全一致的结果,并得到了小球转动的一些规律. 最后根据实验以及数值模拟结果总结了小球被挤出难易程度与模型参数之间的一些关系.

     

    Abstract: Towards a list of rigid balls in inclined V-trough,experiments indicate that the motion shows some instability, namely, thesecond ball will be extruded from the V-trough when the initial number ofballs is odd, while the third will be extruded when the initial number iseven. Considering the column friction between contacts, numerical simulationswere made for this interesting phenomenon. The results areconsistent with experiments very well, thus leading toa few rules in rotation of balls. In the end,the relation between parameters and the degree at which a ball issubjected to extrusion are summarized according to experiments andnumerical simulations.

     

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