Transversal stability of the bouncing ball on a concave surface

Area of Science:

• Nonlinear dynamics
• Chaos theory
• Granular physics

Background:

• The bouncing ball problem illustrates chaos via period doubling.
• Concave surfaces are used to prevent ball escape in experiments.
• Existing models do not fully explain observed experimental instabilities.

Purpose of the Study:

• Investigate the instability observed in the bouncing ball experiment.
• Develop theoretical arguments for the observed pendular motion.
• Explore the system's sensitivity to contact physics.

Main Methods:

• Experimental observation of a bouncing ball on a vibrating surface.
• Theoretical analysis of system dynamics and trajectory.
• Analysis of the effect of vibration frequency on instability.

Main Results:

• The bouncing ball system exhibits instability, deviating from the central axis.
• A pendular motion is observed in the permanent regime.
• Theoretical arguments explain the decrease in trajectory size with increased frequency.

Conclusions:

• The instability is sensitive to contact physics, offering a new experimental probe.
• The system can be used to study collision rules.
• It provides a testbed for numerical simulations of granular matter.