The inverted pendulum: A singularity theory approach
type: Item
instance of: scholarly article
title: The inverted pendulum: A singularity theory approach
zbMATH Open document ID: 0936.34029
published in: Journal of Differential Equations
publication date: 2000-05-08T00:00:00Z
full work available at URL: 1999JDiffEqBroer.pdf
review text: The authors study problems of parametrically forced Hamiltonian systems with an example of the inverted pendulum with small parametric forcing. The qualitative dynamics of the Poincaré map corresponding to the central periodic solution is studied via an approximating integrable normal form. The relation between the Poincaré map and its approximation is discussed in terms of perturbation theory. At bifurcation points local universal models are constructed in an appropriate symmetry context by using methods and techniques from the equivariant singularity theory.
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 37G05
Mathematics Subject Classification ID: 34D15
Mathematics Subject Classification ID: 37J20
Mathematics Subject Classification ID: 37J25
Mathematics Subject Classification ID: 37J40
Mathematics Subject Classification ID: 58K99
zbMATH DE Number: 1346395
zbMATH Keywords: inverted pendulum
zbMATH Keywords: Hamiltonian system
zbMATH Keywords: equivariant singularity
author: Henk Broer
author: Igor Hoveijn
author: Martijn van Noort
author: Gert Vegter
reviewed by: Jiancheng Zou
describes a project that uses: DSTool
MaRDI profile type: Publication
OpenAlex ID: W2098538867
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DOI: 10.1006/JDEQ.1998.3623
description: scientific article; zbMATH DE number 1346395