Differential Equations

, Volume 47, Issue 1, pp 29–37 | Cite as

Chaos in vibroimpact systems with one degree of freedom in a neighborhood of chatter generation: II

  • S. G. Kryzhevich
Ordinary Differential Equations

Abstract

We study the rectilinear motion of a mass point with impacts against a stopper. The motion between the impacts is described by a second-order ordinary differential equation with a parameter. The impact recovery coefficient also depends on the parameter of the vibroimpact system. We describe a bifurcation that leads to the generation of a Smale horseshoe in a parametric neighborhood of the chatter phenomenon. We prove the existence of an invariant set described by symbolic dynamics.

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References

  1. 1.
    Kryzhevich, S.G., Chaos in Vibroimpact Systems with One Degree of Freedom in a Neighborhood of Chatter Generation. I, Differ. Uravn., 2010, vol. 46, no. 10, pp. 1403–1408.Google Scholar
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    Kryzhevich, S.G., Grazing Bifurcation and Chaotic Oscillations of Vibroimpact Systems with One Degree of Freedom, Prikl. Mat. Mekh., 2008, vol. 72, no. 4, pp. 539–556.MathSciNetGoogle Scholar
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    Kryzhevich, S.G. and Pliss, V.A., Chaotic Models of Oscillations of a Vibroimpact System, Prikl. Mat. Mekh., 2005, vol. 69, no. 2, pp. 15–29.MathSciNetGoogle Scholar
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Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  • S. G. Kryzhevich
    • 1
  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

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