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

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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.

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Authors and Affiliations

  1. Department of Physics, Harbin Institute of Technology, Harbin, 150001, P.R. China

    Hong Han, Zehui Jiang, Rui Zhang & Jing Lyu

Authors
  1. Hong Han
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  2. Zehui Jiang
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  3. Rui Zhang
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  4. Jing Lyu
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Correspondence to Zehui Jiang.

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Han, H., Jiang, Z., Zhang, R. et al. Subharmonic bifurcations and chaotic dynamics of an air damping completely inelastic bouncing ball. Eur. Phys. J. B 86, 487 (2013). https://doi.org/10.1140/epjb/e2013-40675-0

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