Applications of the singular value decomposition in dynamics
type: Item
instance of: scholarly article
title: Applications of the singular value decomposition in dynamics
zbMATH Open document ID: 0768.70001
DOI: 10.1016/0045-7825(93)90044-X
author: J. P. Meijaard
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1993-05-16T00:00:00Z
review text: This article presents some applications of the singular value decomposition of a general rectangular matrix for determining solutions of underdetermined systems which arise in the study of dynamical mechanical systems. First, the theory of the singular value decomposition is exposed briefly. Then, it is shown how periodic solutions of Hamiltonian, conservative systems can be determined in a direct way. Finally, a path following method for the continuation of stationary and periodic solutions and bifurcation points is described. The usefulness of these procedures is shown in examples of a rotor with nonlinear support stiffness and a system which consists of an array of ten nonlinearly coupled oscillators.
Mathematics Subject Classification ID: 70-08
Mathematics Subject Classification ID: 70K99
Mathematics Subject Classification ID: 70H05
Mathematics Subject Classification ID: 65F30
zbMATH DE Number: 168852
zbMATH Keywords: underdetermined systems
zbMATH Keywords: periodic solutions
zbMATH Keywords: conservative systems
zbMATH Keywords: path following method
zbMATH Keywords: bifurcation points
zbMATH Keywords: rotor with nonlinear support stiffness
zbMATH Keywords: ten nonlinearly coupled oscillators
describes a project that uses: PITCON
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 168852