A note on circulatory systems: Old and new results

Circulatory systems

Wolfhard Kliem, Christian Pommer

Research output: Contribution to journalJournal articleResearchpeer-review

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Abstract

It is astonishing that after more than half a century intensive research in the area of non-conservative systems of second order differential equations still new interesting results appear, see [4]. In that paper an old stability criterion by Metelitsyn [8] and Frik [9] was reinvented. We shortly repeat this result in order to emphasize that the criterion is sufficient but not necessary for stability. Afterwards we concentrate on circulatory systems with purely imaginary eigenvalues and investigate the influence of indefinite damping. Finally the possibility of stabilizing circulatory systems by gyroscopic forces will be commented. Examples will demonstrate the developed theory.
Original languageEnglish
JournalZeitschrift fuer Angewandte Mathematik und Mechanik
Volume97
Issue number1
Pages (from-to)92–97
ISSN0044-2267
DOIs
Publication statusPublished - 2017

Keywords

  • Ciculatory systems
  • Stability
  • Indefinte damping
  • Gyroscopic damping

Cite this

Kliem, Wolfhard ; Pommer, Christian. / A note on circulatory systems: Old and new results : Circulatory systems. In: Zeitschrift fuer Angewandte Mathematik und Mechanik. 2017 ; Vol. 97, No. 1. pp. 92–97.
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A note on circulatory systems: Old and new results : Circulatory systems. / Kliem, Wolfhard; Pommer, Christian.

In: Zeitschrift fuer Angewandte Mathematik und Mechanik, Vol. 97, No. 1, 2017, p. 92–97.

Research output: Contribution to journalJournal articleResearchpeer-review

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AU - Kliem, Wolfhard

AU - Pommer, Christian

PY - 2017

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N2 - It is astonishing that after more than half a century intensive research in the area of non-conservative systems of second order differential equations still new interesting results appear, see [4]. In that paper an old stability criterion by Metelitsyn [8] and Frik [9] was reinvented. We shortly repeat this result in order to emphasize that the criterion is sufficient but not necessary for stability. Afterwards we concentrate on circulatory systems with purely imaginary eigenvalues and investigate the influence of indefinite damping. Finally the possibility of stabilizing circulatory systems by gyroscopic forces will be commented. Examples will demonstrate the developed theory.

AB - It is astonishing that after more than half a century intensive research in the area of non-conservative systems of second order differential equations still new interesting results appear, see [4]. In that paper an old stability criterion by Metelitsyn [8] and Frik [9] was reinvented. We shortly repeat this result in order to emphasize that the criterion is sufficient but not necessary for stability. Afterwards we concentrate on circulatory systems with purely imaginary eigenvalues and investigate the influence of indefinite damping. Finally the possibility of stabilizing circulatory systems by gyroscopic forces will be commented. Examples will demonstrate the developed theory.

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KW - Indefinte damping

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