Paper Title:
Decoupling the Equations of Isospectral Flow
  Abstract

Three (m × n) matrices {K, D, M} represent a second-order system in the form (K + Dλ+ Mλ2). If m = n, system eigenvalues are defined as the values of λ for which det(K + Dλ+ Mλ2) = 0. If {K, D, M} are continuous functions of a real scalar parameter, σ, eigenvalues and dimensions of the associated eigenspaces remain constant if and only if the rates of change of {K, D, M} obey certain ODEs called the isospectral flow equations. The integration of these matrix differential equations is of interest here. This paper explains the motivation behind this work in terms of vibrating systems and it reports two related hypotheses concerning how the solutions to these equations may be decoupled. Work underway towards proving and using these hypotheses is presented. No existing known solutions allow this decoupling in general.

  Info
Periodical
Edited by
Patrick Sean Keogh
Pages
481-490
DOI
10.4028/www.scientific.net/AMM.5-6.481
Citation
S. D. Garvey, P. Van Eetvelt, U. Prells, "Decoupling the Equations of Isospectral Flow", Applied Mechanics and Materials, Vols. 5-6, pp. 481-490, 2006
Online since
October 2006
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