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A two time scale analysis of gyroscopic motion with friction

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Abstract

The motion of a symmetric rigid body having one fixed point and subject to frictional forces is considered. The frictional forces are due to a surrounding dissipative medium and are accounted for by a model wherein the frictional torque is proportional to the angular velocity. A two time scale perturbation technique is used to analyze and characterize possible motions. The results of calculations which illustrate some of these motions are provided. These results show full agreement with qualitative observations.

Résumé

On considère le mouvement d'un corps rigide symétrique ayant un point fixe et sujet à des forces de friction. Les forces de friction sont dues à un milieu dissipatif et sont représentées par un modèle où le moment de friction est proportionnel à la vitesse angulaire. On utilise une technique de perturbations à double échelle pour l'analyse et la charactérisation des mouvements possibles. On donne des résultats numériques illustrant certains de ces mouvements. Ces résultats sont en accord complet avec les observations qualitatives.

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Authors and Affiliations

  1. Dept. of Mathematics, University of Tennessee, Knoxville, Tennessee

    Henry C. Simpson

  2. Dept. of Mathematics, Carnegie-Mellon University, Pittsburgh, Pennsylvania, USA

    Max D. Gunzburger

Authors
  1. Henry C. Simpson
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  2. Max D. Gunzburger
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Simpson, H.C., Gunzburger, M.D. A two time scale analysis of gyroscopic motion with friction. Journal of Applied Mathematics and Physics (ZAMP) 37, 867–894 (1986). https://doi.org/10.1007/BF00953678

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  • DOI: https://doi.org/10.1007/BF00953678

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