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


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.


Initial Data Unstable Manifold Stable Manifold Symbolic Dynamic Impact Time 
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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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