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Subharmonic bifurcations and chaotic dynamics of an air damping completely inelastic bouncing ball

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  • Hong Han
  • Zehui Jiang
  • Rui Zhang
  • Jing Lyu

Abstract

We investigate the dynamics of a plastic ball on a vibrated platform in air by introducing air damping effect into the completely inelastic bouncing ball model. The air damping gives rise to larger saddle-node bifurcation points and a chaos confirmed by the largest Lyapunov exponent of a one-dimensional discrete mapping. The calculated bifurcation point distribution shows that the periodic motion of the ball is suppressed and a chaos emerges earlier for an increasing air damping. When the reset mechanism and the linear stability which cause periodic motion of the ball both collapse, the investigated system is fully chaotic. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Hong Han & Zehui Jiang & Rui Zhang & Jing Lyu, 2013. "Subharmonic bifurcations and chaotic dynamics of an air damping completely inelastic bouncing ball," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 86(12), pages 1-7, December.
    • Handle: RePEc:spr:eurphb:v:86:y:2013:i:12:p:1-7:10.1140/epjb/e2013-40675-0
    DOI: 10.1140/epjb/e2013-40675-0
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    Cited by:

    1. Han, Hong & Jiang, Ze Hui & Zhang, Rui & Lyu, Jing, 2014. "The influence of air on period doubling motion in vertically vibrated grains beds," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 403(C), pages 265-275.
    2. Dong, Jinlu & Fang, Jianhong & Pan, Jingwu & Hong, Guangyang & Li, Jian, 2022. "Dynamic model of vibrating plate coupled with a granule bed," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).

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    Keywords

    Statistical and Nonlinear Physics;

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