Grazing in Impact Oscillators

Part of the NATO ASI Series book series (ASIC, volume 464)


In the last talk on impact oscillators we reviewed some of their general behaviour and looked at the simple smooth bifurcations that occur when studying the stability of the simple (1, n) orbits. We now proceed to investigate the bifurcations which can occur when we consider discontinuous changes in behaviour. These are associated with grazing impacts of the trajectory of the particle with the obstacle. A graze leads to quite remarkable behaviour including an immediate bifurcation from a periodic orbit to a chaotic one. Such behaviour is unique to impact oscillators although [Nordmark] has shown that some of the behaviour associated with the discontinuities in the impact oscillator can be viewed as a limit of smooth bifurcations occuring in systems with smooth models for the impacts.


Periodic Orbit Velocity Impact Chaotic Behaviour Stable Manifold Strange Attractor 
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  1. Most of the references are given in the notes to the previous talk, some new ones related to grazing are the followingGoogle Scholar
  2. Budd, C. and Dux, F. b Intermittency in impact oscillators close to resonance Bristol University Report AM-93–14, 1993.Google Scholar
  3. Nusse, H, Ott, E. and Yorke, J. Border-collision bifurcations: a possible explanation for observed bifurcation phenomena, University of Maryland report, 1993.Google Scholar
  4. Pomeau, Y. and Manneville, P. Intermittent transition to turbulence in dissipative dynamical systems Comm. Math. Phys., 84, 1980, 189.MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1995

Authors and Affiliations

  1. 1.School of Mathematics University of BristolUniversity WalkBristolUK

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