Nonlinear Dynamics

, Volume 10, Issue 1, pp 63–87 | Cite as

Some aspects of destabilization in reversible dynamical systems with application to follower forces

  • O. M. O'Reilly
  • N. K. Malhotra
  • N. S. Namachchivaya


This paper examines the destabilization of the equilibria of reversible dynamical systems which is induced by the addition of irreversible perturbations. Attention is restricted to reversible dynamical systems which have frequently appeared in the literature on elastic stability. There they are often referred to as follower force problems. The destabilization phenomenon is linear in nature and explicit criteria are established to determine the particular eigenvalue splittings. The post-destabilization dynamics are also examined using the appropriate normal forms for two specific cases, one where the eigenvalues are non-resonant and the other where the eigenvalues are in a strong one-to-one resonance. Finally, the destabilization criteria and certain features of the post-destabilization dynamics are illustrated using two examples of follower force systems.

Key words

Reversible dynamical systems dissipation induced destabilization local bifurcations normal forms 


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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • O. M. O'Reilly
    • 1
  • N. K. Malhotra
    • 2
  • N. S. Namachchivaya
    • 2
  1. 1.Department of Mechanical EngineeringUniversity of California at BerkeleyBerkeleyU.S.A.
  2. 2.Department of Aeronautical and Astronautical EngineeringUniversity of Illinois at Urbana-ChampaignUrbanaU.S.A.

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