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An analytical and numerical study of chaotic dynamics in a simple bouncing ball model

An analytical and numerical study of chaotic dynamics in a simple bouncing ball model
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摘要 Dynamics of a ball moving in gravitational field and colliding with a moving table is studied in this paper. The motion of the limiter is assumed as periodic with piecewise constant velocity—it is assumed that the table moves up with a constant velocity and then moves down with another constant velocity.The Poincaré map,describing evolution from an impact to the next impact,is derived and scenarios of transition to chaotic dynamics are investigated analytically and numerically. Dynamics of a ball moving in gravitational field and colliding with a moving table is studied in this paper. The motion of the limiter is assumed as periodic with piecewise constant velocity—it is assumed that the table moves up with a constant velocity and then moves down with another constant velocity.The Poincaré map,describing evolution from an impact to the next impact,is derived and scenarios of transition to chaotic dynamics are investigated analytically and numerically.
作者 Andrzej Okninski Bogusaw Radziszewski
机构地区 Physics Division Department of Mechatronics and Mechanical Engineering
出处 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2011年第1期130-134,共5页 力学学报（英文版）
关键词 Nonsmooth dynamics · Bouncing ball · Exact solutions Nonsmooth dynamics · Bouncing ball · Exact solutions
分类号 O343 [理学—固体力学]
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参考文献14

  • 1Bernardo, M., Budd, C.J., Champneys, A.R., et al.: Piecewise- Smooth Dynamical Systems. Theory and Applications. Series: Applied Mathematical Sciences, Springer, Berlin (2008).
  • 2Luo, A.C.J.: Singularity and Dynamics on Discontinuous Vector Fields. Monograph Series on Nonlinear Science and Complexity, Elsevier, Amsterdam (2006).
  • 3Awrejcewicz, J., Lamarque, C.-H.: Bifurcation and Chaos in Nonsmooth Mechanical Systems. World Scientific Series on Nonlinear Science: Series A, World Scientific Publishing, Singapore (2003).
  • 4Filippov, A.F.: Differential Equations with Discontinuous Right-Hand Sides. Kluwer Academic, Dordrecht (1988).
  • 5Stronge, W.J.: Impact Mechanics. Cambridge University Press, Cambridge (2000).
  • 6Mehta A.: Granular Matter: An Interdisciplinary Approach. Springer, Berlin (1994).
  • 7Knudsen, C., Feldberg, R., True, H.: Bifurcations and chaos in a model of a rolling wheel-set. Philos. Trans. R. Soc. Lond. A 338,455-469 (1992).
  • 8Wiercigroch, M., Krivtsov, A.M., Wojewoda, J.: Vibrational energy transfer via modulated impacts for percussive drilling. Journal of Theoretical and Applied Mechanics 46, 715-726 (2008).
  • 9Luo, A.C.J., Guo, Y.: Motion switching and chaos of a particle in a generalized fermi-acceleration oscillator, mathematical problems in engineering. 2009. doi: 10.1155/2009/298906.
  • 10Okninski, A., Radziszewski, B.: Chaotic dynamics in a simple bouncing ball model. In: Lodz, Poland,Awrejcewicz, J., Kazmierczak, M., Olejnik, P., et al., eds. Proceedings of the 10th Conference on Dynamical Systems: Theory and Applications, December 7-10, 2009. 651-656.
Acta Mechanica Sinica
2011年 第1期

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