## Abstrakti

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.

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.

Alkuperäiskieli | Englanti |
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Julkaisupaikka | Jyväskylä |

Kustantaja | University of Jyväskylä |

Sivumäärä | 51 |

ISBN (painettu) | 978-951-39-6773-4 |

Tila | Julkaistu - 2016 |

OKM-julkaisutyyppi | D4 Julkaistu kehittämis- tai tutkimusraportti taikka -selvitys |

### Julkaisusarja

Nimi | Reports of the Department of Mathematical Information Technology. Series B, Scientific Computing |
---|---|

Kustantaja | University of Jyväskylä |

Vuosikerta | 9 |

ISSN (painettu) | 1456-436X |