Outlines of the theory of large perturbations of linear systems with finite degrees of freedom

Bosznay, Ádám (2002) Outlines of the theory of large perturbations of linear systems with finite degrees of freedom. JOURNAL OF COMPUTATIONAL AND APPLIED MECHANICS, 3 (2). pp. 117-139. ISSN 1586-2070

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Abstract

The aim of this paper is to give closed, exact and general formulae for the eigenvalues and eigenvectors (in an arbitrarily large measure) of a perturbated conservative linear oscillator, valid also for the case of of invariant (persistent) and degenerated (or having both properties) eigenvalues. Such formulae are established and their properties are investigated. Some special inverse eigenvalue problems are raised and solved based on the formulae established; in this manner a so called deflation can also be solved. We show that the Lancester formula [11] (not systematically derived there) is a special case of our results. We embed these results in some relevant problems of the literature.

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