Euler equations on so(4) as a nearly integrable Hamiltonian system

Guillermo Dávila Rascón, Rubén Flores Espinoza, Yuri M. Vorobiev

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3 Scopus citations


We show that Euler equations on the Lie algebra so(4) near a singular adjoint orbit can be represented as a perturbed Hamiltonian system whose unperturbed part is a completely integrable system, non-degenerate in the sense of Rüssmann. To make this property visible we apply a "twisting" mapping defined as the composition of a Floquet-Lyapunov type transformation and the time-1 flow of a time-dependent dynamical system associated with the Euler equations.

Original languageEnglish
Pages (from-to)129-146
Number of pages18
JournalQualitative Theory of Dynamical Systems
Issue number1
StatePublished - Aug 2008

Bibliographical note

Funding Information:
Partially supported by CONACYT, under grant SEP 2003–CO2–43208.


  • Action-angle variables
  • Hamiltonian system
  • Perturbation
  • Poisson structures
  • Quasi-periodic tori


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