Dynamic Patterns and Self-Knotting of a Driven Hanging Chain

Belmonte, Andrew; Shelley, Michael J.; Eldakar, Shaden T.; Wiggins, Chris H.

When shaken vertically, a hanging chain displays a startling variety of distinct behaviors. We find experimentally that instabilities occur in tonguelike bands of parameter space, to swinging or rotating pendular motion, or to chaotic states. Mathematically, the dynamics are described by a nonlinear wave equation. A linear stability analysis predicts instabilities within the well-known resonance tongues; their boundaries agree very well with experiment. Full simulations of the 3D dynamics reproduce and elucidate many aspects of the experiment. The chain is also observed to tie knots in itself, some quite complex. This is beyond the reach of the current analysis and simulations.



Also Published In

Physical Review Letters

More About This Work

Academic Units
Applied Physics and Applied Mathematics
American Physical Society
Published Here
September 19, 2014