title: Transversal stability of the bouncing ball on a concave surface.
abstract: 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.
authors.affiliation: Université de Lyon, Laboratoire de Physique, Ecole Normale Supérieure de Lyon, CNRS, 46 Allée d'Italie, 69364 Lyon cedex 07, France.
authors.forename: J-Y
authors.initials: JY
authors.lastname: Chastaing
authors.affiliation: Université de Lyon, Laboratoire de Physique, Ecole Normale Supérieure de Lyon, CNRS, 46 Allée d'Italie, 69364 Lyon cedex 07, France.
authors.forename: G
authors.initials: G
authors.lastname: Pillet
authors.affiliation: Université de Lyon, Laboratoire de Physique, Ecole Normale Supérieure de Lyon, CNRS, 46 Allée d'Italie, 69364 Lyon cedex 07, France.|Université de Lyon, UFR de Physique, Université Claude Bernard Lyon I, 69100 Villeurbanne, France.
authors.forename: N
authors.initials: N
authors.lastname: Taberlet
authors.affiliation: Université de Lyon, Laboratoire de Physique, Ecole Normale Supérieure de Lyon, CNRS, 46 Allée d'Italie, 69364 Lyon cedex 07, France.
authors.forename: J-C
authors.initials: JC
authors.lastname: Géminard