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Stochastic dynamics of a rod bouncing upon a vibrating surface
H S Wright1, Michael R Swift, P J King
1School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, United Kingdom.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 7, 2007
Summary
A vibrating surface causes a bouncing rod to transition from predictable to chaotic motion. Impact times and angles follow specific statistical distributions, with energy favoring vertical movement.
Area of Science:
- Physics
- Nonlinear Dynamics
- Statistical Mechanics
Background:
- Understanding the complex dynamics of bouncing objects is crucial in various fields, from granular physics to mechanical engineering.
- Previous studies have explored simple object collisions, but the behavior of elongated objects under vibration remains less understood.
Purpose of the Study:
- To investigate the transition from periodic to stochastic dynamics of a rod bouncing on a vibrating surface.
- To characterize the statistical distributions of impact times, angles, and energy components.
- To determine the influence of parameters like acceleration, rod length, and frequency on these dynamics.
Main Methods:
- Comparison of experimental results with computer simulations.
- Utilizing a stainless-steel rod bouncing on a metal-coated glass surface.
- Varying the dimensionless acceleration parameter (Gamma), rod length, and vibration frequency.
Main Results:
- A transition from periodic to stochastic dynamics was observed as Gamma increased above unity.
- Impact time statistics showed approximate Gaussian tails, while impact angle distributions exhibited near-exponential tails.
- Energy statistics, including translational and rotational components, approximated Boltzmann distributions in their tails.
- Strong correlations were found between translational and rotational energy, with vertical translational energy dominating.
Conclusions:
- The study reveals a clear transition to stochastic behavior in a bouncing rod system under vertical vibration.
- The observed statistical distributions provide a quantitative description of the chaotic dynamics.
- Energy distribution highlights the dominance of vertical motion and strong coupling between translational and rotational components.
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