The Painlevé paradox studied at a 3D slender rod
The Painlevé paradox studied at a 3D slender rod
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DOI：
10.1007/s11044-007-9098-7
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发表时间：
2008-05
影响因子：
3.4
通讯作者：
Zhen Zhao;Caishan Liu;Bin Chen
中科院分区：
文献类型：
--
作者：
Zhen Zhao;Caishan Liu;Bin Chen
研究了具有Painlevé佯谬的三维杆在粗糙表面上运动的动力学行为。根据LCP空间多体系统方法的理论结果，研究了杆中Painlevé佯谬发生的条件。通过将柔顺接触模型插入到刚体模型中得到的数值结果支持切向冲击与空间矛盾情况有关的假设。此外，切向冲击分析使用Darboux-Keller的冲击动力学，并发现具有相同的性质，在平面杆的一个：一个切向棒出现在接触点的冲击过程中。借助Stronge系数，建立了一个描述三维杆在奇异情况下动力学行为的碰撞规则。达布模型和柔顺接触模型的数值结果进行了比较，并显示出良好的协议。
This paper aims at investigating the dynamical behaviors of a 3D rod moving on a rough surface with so-called Painlevé paradox. The condition for the occurrence of the Painlevé paradox in the rod is studied according to the theoretical results obtained from LCP’s method for spatial multibody systems. Numerical results obtained by inserting a compliant contact model into the rigid body model present a support for the assumption that a tangential impact is related to the spatial paradoxical situations. Furthermore, the tangential impact is analyzed by using the Darboux–Keller’s shock dynamics and are found with the same properties as the one in the planar rod:A tangential stick appears at the contact point during the impulsive process. With the help of the Stronge’s coefficient, an impact rule is developed to describe the dynamical behaviors of the 3D rod with paradoxical situations. Comparisons between numerical results obtained from Darboux’s model and the ones obtained from the compliant contact model are carried out and show well agreements.