柔性体的拾取和撞击
Pick-up and impact of flexible bodies
摘要：
拾取、放下、碰撞、滚动和剥离是涉及移动不连续性的部分接触相互作用。我们研究的平衡的动量和能量跨越一个移动的不连续性，在一个字符串，与津贴的注入或耗散的奇异供应。我们分裂的能量耗散，根据其不变性的性质，讨论与系统的粒子和连接与文献中的冲击和相变前线在各种机构的类比，并推导出一个兼容的供应之间的关系的动量和耗散不变的能量。对于一个移动的接触不连续性之间的字符串和一个光滑的刚性平面在重力的存在下，我们发现一个令人惊讶的不对称性之间的过程中，拿起和放下，这样的稳定状态扭结的几何形状和相关的跳跃张力是不允许在拿起。这一预测与实验观察结果一致。我们简要地讨论了有关的问题，包括下降的折叠链，剥离的胶带，和“链喷泉”。我们的方法是适用于研究的影响和运动，以及系统，如系泊的浮动结构和一些乐器，具有振动的字符串和电缆元件与表面相互作用。
英文摘要：
Picking up, laying down, colliding, rolling, and peeling are partial-contact interactions involving moving discontinuities. We examine the balances of momentum and energy across a moving discontinuity in a string, with allowance for injection or dissipation by singular supplies. We split the energy dissipation according to its invariance properties, discuss analogies with systems of particles and connections with the literature on shocks and phase transition fronts in various bodies, and derive a compatibility relation between supplies of momentum and translation-invariant energy. For a moving contact discontinuity between a string and a smooth rigid plane in the presence of gravity, we find a surprising asymmetry between the processes of picking up and laying down, such that steady-state kinks in geometry and associated jumps in tension are not admissible during pick-up. This prediction is consistent with experimental observations. We briefly discuss related problems including the falling folded chain, peeling of an adhesive tape, and the "chain fountain". Our approach is applicable to the study of impact and locomotion, and to systems such as moored floating structures and some musical instruments that feature vibrating string and cable elements interacting with a surface.
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