牛顿摆的同步行为
Synchronization Behavior of Newton's Cradle
AI总结：
本文将牛顿摆建模为进行粘弹性碰撞的非线性弹簧摆集合，发现径向与角运动的共振会调制同步速率，所提理论为同步运动提供了出色的长期预测。
摘要：
牛顿摆是一种利用一系列相同碰撞摆来演示动量守恒的装置。尽管它是演示动量守恒概念的著名例子，但文献中极少报道对该系统的深入分析。在此，我们将该系统建模为进行粘弹性碰撞的相同非线性弹簧摆集合，这与在各种条件下进行的实验高度吻合。我们详细研究了其同步速率对四个关键系统参数的依赖关系。有趣的是，我们发现径向运动与角运动之间的共振会调制同步速率。充分考虑二维运动和弦迟滞效应的所提理论，为同步后的摆运动提供了出色的长期预测。
英文摘要：
A Newton's cradle is a device that demonstrates conservation of momentum using a series of identical colliding pendula. Despite being a famous example that demonstrates the concept of momentum conservation, extensive analysis of the system is rarely reported in literature. Here, we model the system as a collection of identical nonlinear spring pendulums performing viscoelastic collisions, which shows excellent agreement with experiments performed at various conditions. Dependence of its synchronization rate on four key system parameters are studied in detail. Interestingly, the resonance between radial and angular motion was found to modulate the synchronization rate. The proposed theory with full consideration of two dimensional motion and string hysteresis provides an excellent long-term prediction of the synchronized cradle motion.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
