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Decoupling the Equations of Isospectral Flow

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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.

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Periodical:

Applied Mechanics and Materials (Volumes 5-6)

Pages:

481-490

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.5-6.481

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Online since:

October 2006

Authors:

Seamus D. Garvey, Peter Van Eetvelt, U. Prells

Keywords:

Integrable Systems, Nahm's Equations, Proportional Damping

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© 2006 Trans Tech Publications Ltd. All Rights Reserved

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