On the global geometric structure of the dynamics of the elastic pendulum
type: Item
instance of: scholarly article
title: On the global geometric structure of the dynamics of the elastic pendulum
zbMATH Open document ID: 0963.70013
DOI: 10.1023/A:1008356204490
author: Ioannis T. Georgiou
published in: Nonlinear Dynamics
publication date: 2001-06-28T00:00:00Z
review text: The authors studies the dynamics of planar elastic pendulum by considering it as a singular perturbation of uncoupled pendulum. The equations of motion are \(\ddot\theta+ {2\dot\theta \dot R\over 1+R}+ {\sin\theta \over 1+R}=0\) and \(\ddot R+({\omega_s \over\omega_p})^2 R-(1+R_)\dot \theta^2+1-\cos\theta=0\), where \(\omega_p\) and \(\omega_s\) denote respectively natural frequencies of the pendulum and radial oscillator. The author determines the global geometric structure of the dynamics in terms of two-dimensional invariant manifolds of motion. A general analytic study is carried out and confirmed by numerical experiments.
Mathematics Subject Classification ID: 70K05
Mathematics Subject Classification ID: 70K20
Mathematics Subject Classification ID: 70K50
Mathematics Subject Classification ID: 70K60
zbMATH DE Number: 1342560
zbMATH Keywords: planar elastic pendulum
zbMATH Keywords: singular perturbation
zbMATH Keywords: global geometric structure
zbMATH Keywords: two-dimensional invariant manifolds of motion
reviewed by: Silvio Nocilla
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1342560