Dissipation-induced heteroclinic orbits in tippe tops

Nawaf M. Bou-Rabee, Jerrold E. Marsden, Louis A. Romero

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


This paper demonstrates that the conditions for the existence of a dissipation-induced heteroclinic orbit between the inverted and noninverted states of a tippe top axe determined by a complex version of the equations for a simple harmonic oscillator: the modified Maxwell-Bloch equations. A standard linear analysis reveals that the modified Maxwell-Bloch equations describe the spectral instability of the noninverted state and Lyapunov stability of the inverted state. Standard nonlinear analysis based on the energy momentum method gives necessary and sufficient conditions for the existence of a dissipation-induced connecting orbit between these relative equilibria.

Original languageEnglish (US)
Pages (from-to)325-344
Number of pages20
JournalSIAM Review
Issue number2
StatePublished - Jun 2008
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computational Mathematics
  • Applied Mathematics


  • Dissipation-induced instability
  • Gyroscopic stabilization
  • Heteroclinic orbits
  • Relative equilibria
  • Tippe top inversion


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