Time-dependent normal form Hamiltonian for dynamical equilibria

Karl Erik Thylwe; Harry Dankowicz

doi:10.1088/0305-4470/29/13/035

Time-dependent normal form Hamiltonian for dynamical equilibria

Karl Erik Thylwe, Harry Dankowicz

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English (US)
Pages (from-to)	3707-3722
Number of pages	16
Journal	Journal of Physics A: Mathematical and General
Volume	29
Issue number	13
DOIs	https://doi.org/10.1088/0305-4470/29/13/035
State	Published - 1996
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy

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10.1088/0305-4470/29/13/035

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abstract = "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.",

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Time-dependent normal form Hamiltonian for dynamical equilibria

Abstract

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