On Unbounded Motions in a Real Analytic Bouncing ball Problem
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Universidad de Oviedo
info
ISSN: 1575-5460
Year of publication: 2022
Volume: 21
Issue: 4
Type: Article
More publications in: Qualitative theory of dynamical systems
Abstract
We consider the model of a ball elastically bouncing on a racket moving in the vertical direction according to a given periodic function f (t). The gravity force is acting on the ball. We prove that if the function f (t) belongs to a class of trigonometric polynomials of degree 2 then there exists a one dimensional continuum of initial conditions for which the velocity of the ball tends to infinity. Our result improves a previous one by Pustyl’nikov and gives a new upper bound to the applicability of KAM theory to this model.
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