Some remarks on the periodic motions of a bouncing ball
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866911760508780544 |
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| author | Marò, Stefano |
| author_facet | Marò, Stefano |
| contents | We consider the vertical motion of a free falling ball bouncing elastically on a racket moving in the vertical direction according to a regular $1$-periodic function $f$. For fixed coprime $p,q$ we study existence, stability in the sense of Lyapunov and multiplicity of $p$ periodic motions making $q$ bounces in a period. If $f$ is real analytic we prove that one periodic motion is unstable and give some information on the set of these motions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_14013 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Some remarks on the periodic motions of a bouncing ball Marò, Stefano Dynamical Systems We consider the vertical motion of a free falling ball bouncing elastically on a racket moving in the vertical direction according to a regular $1$-periodic function $f$. For fixed coprime $p,q$ we study existence, stability in the sense of Lyapunov and multiplicity of $p$ periodic motions making $q$ bounces in a period. If $f$ is real analytic we prove that one periodic motion is unstable and give some information on the set of these motions. |
| title | Some remarks on the periodic motions of a bouncing ball |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2207.14013 |