Time-dependent normal form Hamiltonian for dynamical equilibria

Karl Erik Thylwe, Harry Dankowicz

Research output: Contribution to journalArticlepeer-review


A new time-dependent normal-form procedure for dynamical equilibria (undergoing parametric excitation) of one-dimensional (1D) Hamiltonian systems is developed with the method of Lie transforms. The expansion is based on the Lewis invariant for the linearized motion. The time-dependent Hamiltonian normal form reduces smoothly to the usual representation in the autonomous limit. Illustrative examples of the formalism are focused on time-periodic systems and the dynamics of Hamiltonian switching.

Original languageEnglish (US)
Pages (from-to)3707-3722
Number of pages16
JournalJournal of Physics A: Mathematical and General
Issue number13
StatePublished - 1996
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • General Physics and Astronomy


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