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On the stability of dissipative systems with circulatory forces

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Abstract

The stability of dissipative systems with circulatory forces is revisited. It is found that a general statement recently made by J. Teichmann [6] is erroneous and the validity of a Thompson-Tait-like statement can be derived for less severe conditions (‘semi-autonomous’ systems) than those of P. C. Müller [5].

Zusammenfassung

Die Stabilität eines dissipativen Systems mit zirkulatorischen Kräften wurde unterscht. Es stellt sich heraus, dass eine allgemeine Aussage von J. Teichmann [6] falsch ist, und dass die Gültigkeit einer Stabilitätsaussage in der Art von Thompson-Tait für eine weniger streng (‘halbautonome Systeme’) Bedingung als in P. C. Müller [5] abgeleitet werden kann.

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References

  1. P. C. Müller,Stabilität und Matrizen, Springer-Verlag, Berlin, 1977.

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  2. W. Thompson, P. G. Tait,Treatise on Natural Philosophy, Part 1, Cambridge, 1921.

  3. N. G. Chetaev,Stability of Motion (in Russian), Moscow, 1955.

  4. H. Tasso, Z. für Naturforschung33a, 257, 1978.

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  5. P. C. Müller, ZAMM52, T65 (1972).

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  6. J. Teichmann, Z. Angew. Math. Phys.30, 1027 (1979).

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Authors and Affiliations

  1. Max-Planck-Institut für Plasmaphysik, Association EURATOM-IPP, 8046, Garching b. München, Germany

    H. Tasso

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  1. H. Tasso
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Tasso, H. On the stability of dissipative systems with circulatory forces. Journal of Applied Mathematics and Physics (ZAMP) 31, 536–537 (1980). https://doi.org/10.1007/BF01590865

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  • DOI: https://doi.org/10.1007/BF01590865

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