On the stability and trajectories of the double pendelum with linear springs and dampers

Juha Jeronen, Reijo Juhani Kouhia

    Tutkimustuotos: Tutkimusraportti


    Anomalous dissipation-induced destabilization is investigated in a simple,
    small system consisting of a double pendulum with springs. This report concentrates
    on providing technical details such as the derivation of the model, and
    approaches for its solution. Several variants of the model are considered. Each
    rod in the double pendulum is considered to be rigid, and to have either uniform
    density, or alternatively, all of its mass concentrated at the midpoint. The
    plane of the system is optionally tilted at an angle to the vertical. The gravitational
    loading contribution of the rods is taken into account. Up to two external
    loads may be present. One is gravitational loading by a dead weight placed at
    the free end; the other is a follower force pressing the free end of the system
    inward. The nonlinear dynamical equations are derived using the principle of
    virtual work. A nondimensional form of the problem is given. Conditions for
    static equilibria are determined. A general linearized variant of the model is
    considered for purposes of comparison to classical solutions, and for determining
    the stability of the static equilibria of the system. Finally, some recommendations
    for numerical approaches are given.
    KustantajaUniversity of Jyväskylä
    ISBN (painettu)978-951-39-6773-4
    TilaJulkaistu - 2016
    OKM-julkaisutyyppiD4 Julkaistu kehittämis- tai tutkimusraportti taikka -selvitys


    NimiReports of the Department of Mathematical Information Technology. Series B, Scientific Computing
    KustantajaUniversity of Jyväskylä
    ISSN (painettu)1456-436X


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