The Dynamics of the Chain Fountain

A fast-falling chain of beads from a raised container could form a fountain-like hoisted arch in the air. This so-called chain fountain phenomenon has baffled the public and the scientific community for almost a decade since it was first demonstrated by Steve Mould in 2013 and has attracted worldwide attention through rampant media broadcasting. However, its quirky behavior has led to erroneous explanations from the researchers as attested by all the relevant publications so far, mainly owing to its sensitive dependence upon the temporal variations of key variables due to the highly nonlinear dynamic nature of the motion. In this paper, by ignoring the irregularity of the movement caused by the layout of the chain in the container, a complete set of the governing nonlinear differential equations are derived, based on which the mechanism of the chain fountain is analyzed, and the acquired knowledge is further extended to discuss more general phenomena in nature and human world.