Indefinite damping in mechanical systems and gyroscopic stabilization

Wolfhard Kliem, Christian Pommer

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    Abstract

    This paper deals with gyroscopic stabilization of the unstable system Mx + D(x) over dot + K-x = 0, with positive definite mass and stiffness matrices M and K, respectively, and an indefinite damping matrix D. The main question if for which skew-symmetric matrices G the system Mx (D+ G)(x) over dot + K-x = 0 can become stable? After investigating special cases we find an appropriat solution of the Lyapunov matrix equation for the general case. Examples show the deviation of the stability limit found by the Lyapunov method from the exact value.
    Original languageEnglish
    JournalZeitschrift fuer Angewandte Mathematik und Physik
    Volume60
    Issue number4
    Pages (from-to)785-795
    ISSN0044-2275
    DOIs
    Publication statusPublished - 2009

    Keywords

    • stability
    • Lyapunov's matrix equation
    • Indefinite damping

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