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Chaos / Volume 22 / Issue 1 / REGULAR ARTICLES

Chaos 22, 013106 (2012); http://dx.doi.org/10.1063/1.3673786 (6 pages)

Saddle-point solutions and grazing bifurcations in an impacting system

Joanna F. Mason and Petri T. Piiroinen

School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, University Road, Galway, Ireland

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(Received 14 July 2011; accepted 10 December 2011; published online 13 January 2012)

This paper focuses on the intricate relationship between smooth and nonsmooth phenomena in an impacting system. In particular a boundary saddle-point solution, that is born in a nonsmooth fold, is analysed. Accessible boundary saddle-point solutions play a key role in determining the global dynamics of a system and here we will show how grazing bifurcations can affect their existence.

© 2012 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. DYNAMICS
    1. The impact map
    2. Quiet operation and periodic orbits
  3. RESULTS
    1. Accessible boundary saddle-point solutions
    2. Codimension-two bifurcations
    3. Nonsmooth folds
  4. DISCUSSION

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KEYWORDS and PACS

Keywords

bifurcation, impact (mechanical)

PACS

  • 05.45.-a

    Nonlinear dynamics and chaos

  • 45.40.-f

    Dynamics and kinematics of rigid bodies

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3673786

PUBLICATION DATA

ISSN

1054-1500 (print)  
1089-7682 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    J. Thompson and R. Ghaffari, Phys. Rev. A 27, 1741 (1982).

    J. F. Mason and P. T. Piiroinen, Chaos 21(1), 013113 (2011)CHAOEH000021000001013113000001.

    H. M. Osinga, Phys. Rev. E 74, 035201(R) (2006).


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