Gyroscopic stabilization and indefimite damped systems

Christian Pommer

    Research output: Contribution to conferenceConference abstract for conferenceResearch

    Abstract

    An important issue is how to modify a given unstable matrix in such a way that the resulting matrix is stable. We investigate in general under which condition a matrix M+A is stable,where M is an arbitrary matrix and A is skew-Hermitian. We show that if trace(M) > 0 it is always possible to find a class of feasibel skew-Hermitian matrices A depending on the choise of M. The theory can be applied to dynamical systems of the form x''(t) + ( dD + g G) x'(t) + K x(t) = 0 where G is a skew symmetric gyrocopic matrix, D is a symmetric indefinite damping matrix and K > 0 is a positive definite stiffness matrix. d and g are scaling factors used to control the stability of the system. It is quite astonnishing that when the damping matrix D is indefinite the system can under certain conditions be stable even if there are no gyroscopic forces G present The Lyapunov matrix equation is used to predict the stabilty limit for pure dissipative systems as well as for dissipative systems with gyroscopic stabilization.
    Original languageEnglish
    Publication date2006
    Publication statusPublished - 2006
    EventJoint GAMM-SIAM Conference on Applied Linear Algebra - University of Düsseldorf, Germany
    Duration: 1 Jan 2006 → …

    Conference

    ConferenceJoint GAMM-SIAM Conference on Applied Linear Algebra
    CityUniversity of Düsseldorf, Germany
    Period01/01/2006 → …

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