Bifurcations in gyroscopic systems with an application to rotating shafts

Wayne Nagata, N. Sri Namachchivaya

Research output: Contribution to journalArticlepeer-review


In this paper we study discrete nonlinear gyroscopic systems which can be obtained either in the context of rigid-body motions or by applying the Galerkin approximation to continuous systems. The problem considered in this paper is motivated by the whirling motion of a rotating shaft which is a fundamental component of many mechanical systems. The aim of our work is to study the effects of small dissipative and symmetry-breaking perturbations on bifurcations in gyroscopic systems, when the unperturbed Hamiltonian system with symmetry exhibits either a double zero or one-to-one resonance instability. Dissipative and symmetry-breaking perturbations, arising from imperfections inherent in most practical mechanical systems, can give rise to both local and global bifurcations. The general theoretical results for the two-degree-of-freedom gyroscopic systems are finally applied to study the dynamics of a rotating shaft.

Original languageEnglish (US)
Pages (from-to)543-585
Number of pages43
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number1970
StatePublished - 1998
Externally publishedYes


  • Bifurcations
  • Dissipative and symmetry-breaking perturbations
  • Gyroscopic systems
  • Nonlinear dynamics
  • Normal forms

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)


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