We consider the model describing the vertical motion of a ball falling with constant acceleration on a wall and elastically reflected. The wall is supposed to move in the vertical direction according to a given periodic function f. We apply the Aubry-Mather theory to the generating function in order to prove the existence of bounded motions with prescribed mean time between the bounces. As the existence of unbounded motions is known, it is possible to find a class of functions f that allow both bounded and unbounded motions. © 2013 IOP Publishing Ltd & London Mathematical Society.
Coexistence of bounded and unbounded motions in a bouncing ball model
Marò, Stefano
Primo
2013-01-01
Abstract
We consider the model describing the vertical motion of a ball falling with constant acceleration on a wall and elastically reflected. The wall is supposed to move in the vertical direction according to a given periodic function f. We apply the Aubry-Mather theory to the generating function in order to prove the existence of bounded motions with prescribed mean time between the bounces. As the existence of unbounded motions is known, it is possible to find a class of functions f that allow both bounded and unbounded motions. © 2013 IOP Publishing Ltd & London Mathematical Society.File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
post_print_Nonlinearity.pdf
accesso aperto
Tipologia:
Documento in Post-print
Licenza:
Creative commons
Dimensione
250.59 kB
Formato
Adobe PDF
|
250.59 kB | Adobe PDF | Visualizza/Apri |
|
Marò_2013_Nonlinearity_version of record.pdf
non disponibili
Tipologia:
Versione finale editoriale
Licenza:
NON PUBBLICO - accesso privato/ristretto
Dimensione
316.44 kB
Formato
Adobe PDF
|
316.44 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
