KAM theory, Lindstedt series and the stability of the upside-down pendulum
type: Item
instance of: scholarly article
title: KAM theory, Lindstedt series and the stability of the upside-down pendulum
zbMATH Open document ID: 1026.37052
author: Kyriakos V. Georgiou
author: Michele Bartuccelli
author: Guido Gentile
published in: Discrete and Continuous Dynamical Systems
publication date: 2003-07-15T00:00:00Z
review text: The present paper deals with a planar pendulum with support point oscillating with a frequency \(\omega\) large enough in the vertical direction. It is well known that the upside-down position of the pendulum corresponds to an equilibrium point for the projection of the motion on the pendulum phase space. The stability of the upside-down position has been proven by the averaging method. In contrast to the averaging method, the authors in this paper show that such an equilibrium point is stable by using the Lindstedt series method and by proving the persistence of invariant KAM tori for the two-dimensional Hamiltonian system describing the model. The authors give four appendices for explaining the proof.
reviewed by: Rong Yuan
Mathematics Subject Classification ID: 37J40
Mathematics Subject Classification ID: 34C15
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 70K40
zbMATH DE Number: 1890745
zbMATH Keywords: upside-down pendulum
zbMATH Keywords: KAM theory
zbMATH Keywords: Lindstedt series
zbMATH Keywords: stability
MaRDI profile type: Publication
full work available at URL: dcds.2003.9.413
OpenAlex ID: W2072981842
DOI: 10.3934/DCDS.2003.9.413
description: scientific article; zbMATH DE number 1890745