Stability of normal modes and subharmonic bifurcations in the 3-body Stokeslet problem
type: Item
instance of: scholarly article
title: Stability of normal modes and subharmonic bifurcations in the 3-body Stokeslet problem
zbMATH Open document ID: 0837.34045
author: Chjan C. Lim
author: I-Heng McComb
published in: Journal of Differential Equations
publication date: 1996-04-23T00:00:00Z
review text: The authors investigate a model related to the sedimentation under gravity of spheres in a highly viscous fluid. Motivated by experimental and analytic investigations they study the motions of 3 identical point particles. Due to the symmetry of the model it is possibly to reduce the originally 6-dimensional system of ODEs with one conserved quantity to a 2-dimensional fixed point space of synchronous or asynchronous solutions, where phase plane analysis can be applied. By calculating the small oscillations close to the synchronous and asynchronous periodic orbits it is shown that the synchronous solutions are elliptic and infinitely many branches of subharmonic solutions bifurcate from these normal modes.
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34C20
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 70F07
Mathematics Subject Classification ID: 76D99
zbMATH DE Number: 806444
zbMATH Keywords: Stokeslet
zbMATH Keywords: subharmonic bifurcation
zbMATH Keywords: normal modes
zbMATH Keywords: sedimentation
zbMATH Keywords: symmetry
zbMATH Keywords: synchronous and asynchronous periodic orbits
reviewed by: Alois Steindl
MaRDI profile type: Publication
OpenAlex ID: W2079747217
DOI: 10.1006/JDEQ.1995.1133
description: scientific article; zbMATH DE number 806444