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Periodicity and bifurcation of a bouncing ball system with rigidly connected harmonic limiters

Ruihai Li

https://orcid.org/0000-0002-1355-7532

School of Mathematics, Harbin Institute of Technology, Harbin 150001, China

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and

Ruiyang Qiu

School of Astronautics, Harbin Institute of Technology, Harbin 150001, China

E-mail Address: 1190100115@stu.hit.edu.cn

Corresponding author.

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https://doi.org/10.1142/S0217984921500664Cited by:0 (Source: Crossref)

Abstract

The bouncing ball system with two rigidly connected harmonic limiters is revisited in order to further analyze its periodic movement and bifurcation dynamics. By using the impulsive impact maps, we obtain several sufficient conditions for the existence and local stability of three different types of periodic orbits, respectively, and then plot the bifurcation diagrams in the space of the relative velocity and the restitution coefficient for different parameters of the limiter. The numerical simulation results are consistent with those of the theoretical analysis.

Keywords:

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