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Chaotic dynamics of an air-damped bouncing ball
M A Naylor1, P Sánchez, Michael R Swift
1School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom.
Summary
Air damping in a bouncing ball system introduces complex dynamics, including chaotic trajectories. This contrasts with simpler models and highlights air effects crucial for understanding fine particulate systems.
Area of Science:
- Physics
- Nonlinear Dynamics
- Fluid Dynamics
Background:
- Bouncing ball systems are classic models for studying chaotic dynamics.
- Introducing a coefficient of restitution leads to periodic behavior, suppressing chaos.
- The influence of air damping on these systems remains incompletely understood.
Purpose of the Study:
- To investigate the dynamical behavior of a vertically vibrated bouncing ball system with air damping.
- To analyze the effects of both static air and air moving with the platform.
- To establish a mapping between different air damping scenarios.
Main Methods:
- Numerical simulations of a bouncing ball model incorporating air resistance.
- Analysis of system trajectories under varying air damping conditions.
- Mathematical derivation of the mapping between static and moving air effects.
Main Results:
- Air damping significantly alters the system's dynamics, reintroducing complex behaviors.
- Both static and moving air damping lead to intricate dynamical regimes, including chaos.
- An exact mapping between static and moving air damping scenarios was identified.
Conclusions:
- Air damping is a critical factor in the dynamics of bouncing ball systems, capable of generating chaotic motion.
- The findings are relevant for understanding the behavior of fine particulate matter in similar environments.
- The established mapping provides a simplified approach to analyzing systems with different air flow conditions.