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Tristability in the pendula chain.

Ramaz Khomeriki1, Jérôme Leon

  • 1Physics Department, Tbilisi State University, 0128 Tbilisi, Georgia and Max-Planck-Institut fur Physik komplexer Systeme, 01187 Dresden, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 31, 2008
PubMed
Summary
This summary is machine-generated.

This study shows a chain of coupled pendula can act as a frequency divider. It achieves an output frequency that is an odd fraction of the driving frequency, demonstrating tristable states.

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Area of Science:

  • Nonlinear dynamics
  • Complex systems
  • Classical mechanics

Background:

  • Coupled pendula systems exhibit complex behaviors under periodic driving.
  • Understanding frequency division in nonlinear systems is crucial for signal processing and chaos control.

Purpose of the Study:

  • To investigate the frequency division capabilities of a short chain of coupled pendula.
  • To identify and characterize the stationary states achieved in such a system.
  • To model the observed phenomena using analytical solutions.

Main Methods:

  • Experimental setup with a periodically driven chain of coupled pendula.
  • Numerical simulations to obtain stationary states.
  • Analytical modeling using the continuous sine-Gordon equation.

Main Results:

  • Demonstrated a regime producing output frequencies at odd fractions of the driving frequency.
  • Identified kinklike motion in the restricted geometry as the mechanism for stationary states.
  • Showcased tristable stationary states in the short pendula chain.
  • Confirmed the system's function as a frequency divider.

Conclusions:

  • The coupled pendula chain exhibits frequency division through tristable states.
  • The observed dynamics are accurately modeled by the sine-Gordon equation, differing from synchronization-based models.
  • This system offers a novel approach to frequency division in nonlinear mechanics.