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Updated: Jul 11, 2026
05:04
Bouncing Ball with a Uniformly Varying Velocity in a Metronome Synchronization Task
Published on: September 21, 2017
Inelastic collapse of a ball bouncing on a randomly vibrating platform
Satya N Majumdar1, Michael J Kearney
1Laboratoire de Physique Théorique et Modèles Statistique, Université Paris-Sud, Bâtiment 100 91405, Orsay Cedex, France. majumdar@lptms.u-psud.fr
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 13, 2007
Summary
This study examines inelastic collisions of a bouncing ball on a vibrating platform. Unlike elastic collisions, inelastic ones result in exponential distributions for flight numbers and collapse times, with universal behavior near the elastic limit.
Area of Science:
- Physics
- Nonlinear Dynamics
- Statistical Mechanics
Background:
- Understanding chaotic dynamics is crucial in physics.
- Bouncing systems exhibit complex behaviors, especially with external stimuli.
- Previous studies focused on elastic collisions, leaving inelastic dynamics less explored.
Purpose of the Study:
- To theoretically investigate the dynamics of a ball undergoing inelastic collisions on a randomly vibrating platform.
- To analyze the distributions of the number of flights and total collapse time.
- To compare the behavior of inelastic collisions with the known power-law distributions of elastic collisions.
Main Methods:
- Theoretical modeling of a bouncing ball system.
- Analysis of probability distributions for key dynamic variables.
- Mathematical derivation of tail behaviors for flight number and collapse time.
Main Results:
- Inelastic collisions lead to exponential tails in distributions, unlike the power-law tails in elastic collisions.
- The decay exponents (theta1, theta2) depend on the coefficient of restitution.
- As the system approaches the elastic limit, these exponents universally vanish.
Conclusions:
- The transition from elastic to inelastic collisions fundamentally alters the statistical properties of the bouncing ball system.
- The nonuniversal nature of the decay exponents highlights the role of inelasticity.
- Universal behavior is observed in the limit of near-elastic collisions.
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