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On the stability of Staude's permanent rotations of a gyroscope with damping

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Summary

The stability behavior of unsymmetric damped gyroscopes varies basically from the well-known behavior of symmetric damped gyroscopes: statically stable gyroscopes may be unstable due to unsymmctries and statically unstable gyroscopes can be stabilized by unsymmetric moments of inertia. The asymptotic stability of unsymmetric gyroscopes is rigorously analysed using the time-invariant equations of motion in a rotating frame and the Hurwitz theorem. The results are presented in the Magnus shape triangle as well for statically stable as for statically unstable gyroscopes.

Übersicht

Das Stabilitätsverhalten des unsymmetrischen gedämpften Kreisels unterscheidet sich grundsätzlich von dem bekannten Verhalten symmetrischer gedämpfter Kreisel: statisch stabile Kreisel können durch die Unsymmetrien instabil werden und statisch instabile Kreisel lassen sich durch unsymmetrische Trägheitsmomente stabilisieren. Die asymptotische Stabilität unsymmetrischer Kreisel wird mit den zeitinvarianten Bewegungsgleichungen im drehenden Bezugssystem vollständig untersucht. Dabei wird das Hurwitzsche Stabilitätskriterium benützt. Die Ergebnisse werden im Magnusschen Formdreieck für statisch stabile und statisch instabile Kreisel dargestellt.

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References

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Authors and Affiliations

  1. Lehrstuhl B für Mechanik, Technische Universität München, Arcisstr. 21, D-8000, München 2, Bundesrepublik Deutschland

    W. O. Schiehlen

  2. Depto. Engenharia Mecanica, Universidade Estadual de Campinas-UNICAMP, Caixa Postal 1170, 13100, Campinas, Brasilien

    H. I. Weber

Authors
  1. W. O. Schiehlen
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  2. H. I. Weber
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Additional information

The authors acknowledge the support of the Deutscher Akademischer Austauschdienst (DAAD), Germany and the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Brazil.

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Schiehlen, W.O., Weber, H.I. On the stability of Staude's permanent rotations of a gyroscope with damping. Ing. arch 46, 281–292 (1977). https://doi.org/10.1007/BF00536482

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  • DOI: https://doi.org/10.1007/BF00536482

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