Transversal stability of the bouncing ball on a concave surface

A ball bouncing repeatedly on a vertically vibrating surface constitutes the famous "bouncing ball" problem, a nonlinear system used in the 1980s, and still in use nowadays, to illustrate the route to chaos by period doubling. In experiments, in order to avoid the ball escape that would be...

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Bibliographic Details
Published in:Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2015-05, Vol.91 (5), p.052918-052918, Article 052918
Main Authors: Chastaing, J-Y, Pillet, G, Taberlet, N, Géminard, J-C
Format: Article
Language:English
Subjects:
General Physics
Physics
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Summary:A ball bouncing repeatedly on a vertically vibrating surface constitutes the famous "bouncing ball" problem, a nonlinear system used in the 1980s, and still in use nowadays, to illustrate the route to chaos by period doubling. In experiments, in order to avoid the ball escape that would be inevitable with a flat surface, a concave lens is often used to limit the horizontal motion. However, we observe experimentally that the system is not stable. The ball departs from the system axis and exhibits a pendular motion in the permanent regime. We propose theoretical arguments to account for the decrease of the growth rate and of the asymptotic-size of the trajectory when the frequency of the vibration is increased. The instability is very sensitive to the physics of the contacts, which makes it a potentially interesting way to study the collisions rules, or to test the laws used in numerical studies of granular matter.
ISSN:1539-3755
1550-2376
DOI:10.1103/PhysRevE.91.052918