Synchronization of perturbed non-linear Hamiltonians
type: Item
instance of: scholarly article
title: Synchronization of perturbed non-linear Hamiltonians
zbMATH Open document ID: 0780.70018
DOI: 10.1007/BF00692993
author: Bruce R. Miller
author: Vincent T. Coppola
published in: Celestial Mechanics and Dynamical Astronomy
publication date: 1993-08-29T00:00:00Z
review text: A method is proposed to simplify perturbed Hamiltonians in one degree of freedom systems by means of (non-canonical) Lie transformations together with a transformation of time. This procedure is chosen to synchronize the motion of the perturbed system with that of its unperturbed part. The method is described algorithmically for Hamiltonians with polynomial potential and demonstrated with perturbed Duffing systems. Relations and differences to ``canonical'' simplifications are discussed.
Mathematics Subject Classification ID: 70H05
Mathematics Subject Classification ID: 70H15
Mathematics Subject Classification ID: 34E10
zbMATH DE Number: 399380
zbMATH Keywords: Lie transformations
zbMATH Keywords: polynomial potential
zbMATH Keywords: perturbed Duffing systems
reviewed by: Michael Baake
describes a project that uses: MACSYMA
MaRDI profile type: Publication
cites work: Q5826059
cites work: Canonical transformations depending on a small parameter
cites work: The main problem of artificial satellite theory for small and moderate eccentricities
cites work: On a perturbation theory using Lie transforms
cites work: A geometric approach to the Ideal Resonance Problem
cites work: A new approach to the librational solution in the Ideal Resonance Problem
cites work: A note on the application of a generalized canonical approach to non-linear Hamiltonian systems
cites work: Q3994364
cites work: Averaging methods in nonlinear dynamical systems
description: scientific article; zbMATH DE number 399380