Dynamic Patterns and Self-Knotting of a Driven Hanging Chain

2001/08/24 by Andrew Belmonte, Michael Shelley, Shaden T. Eldakar +1 · 2 voices · 3 citations
Physics and Astronomy · Computer Science · #Quantum chaos and dynamical systems #Nonlinear Dynamics and Pattern Formation #Chaos control and synchronization

paper · doi:10.1103/physrevlett.87.114301

Abstract

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.

Citations

• Chaos in a double pendulum
• Pattern formation outside of equilibrium

Cited by

• Nonlinear dynamics of a hanging string with a freely pivoting attached mass
• Spontaneous knotting of an agitated string
• The physical consequences of sperm gigantism

Discussions

• Perhaps surprisingly 1 , the literature suggests the dynamics of the suspended string is not chaotic. EDIT: There's a caveat: The paper bellow introduces a relevant model, but its authors are only int [stackexchange, 18 points]
• A $n$ -tuple pendulum is chaotic. Can I approach an ordinary string (no damping) that is vertically hanging by gravity (top end fixed, bottom end free) as an infinitely dense series of pendulums? Is i [stackexchange, 15 points]

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