In this work, we consider the model of a free falling ball on a wall that is elastically reflected. The wall is supposed to move in the vertical direction according to a given quasiperiodic function. Based on the invariant curve theorem of smooth quasiperiodic twist map, we prove the boundedness of all solutions and the existence of quasi-periodic solutions for the system.
This work is supported by the National Natural Science Foundation of China (No. 12172306, 12172167).
Data Availability StatementNo data was used for the research described in the article.
- Bouncing ball
- Invariant curve
- Quasiperiodic motion