Summary
The article deals with dynamical problems of stability of mechanical systems with an infinite number of degrees of freedom, which are acted upon by forces of the dry friction type. Dynamics of a rope moving on a rough flat surface is considered as an example. The article shows that nonhomogeneous properties of friction can result in instability.
Übersicht
Es handelt sich um dynamische Probleme der Stabilität mechanischer Systeme mit unendlich vielen Freiheitsgraden, auf die Kräfte der trockenen Reibung wirken. Die Dynamik eines Seiles, das sich auf einer rauhen Fläche bewegt, wird als Beispiel betrachtet. Es wird gezeigt, daß nichthomogene Eigenschaften der Reibung Instabilität verursachen können.
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References
Lurie, A. I.: Analytical mechanics. Moscow: Fizmatgiz1961 (in Russian)
Smirnow, W. I.: Lehrgang der höheren Mathematik, Band 4, Teil III/2. Berlin: Akademie-Verlag1963
Feldmann, N.: University of Moscow, private communication
Arnold, V. I.: Mathematical methods of classical mechanics. New York: Springer1980
Bogoljubow, N. N.;Mitropolski, J. A.: Asymptotische Methoden in der Theorie der nichtlinearen Schwingungen. Berlin: Akademie-Verlag1965
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This work was supported by the DAAD (der Deutsche Akademische Austauschdienst). I am very grateful to the Director of the Institute B of Mechanics, the University of Stuttgart, Prof. Dr.-Ing. W. Schiehlen for wonderful conditions under which I could work during my stay at his Institute. Without his support, encouragements and useful advice this work could hardly be written.
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Furta, S.D. On the motion of a rope on a rough surface. Arch. Appl. Mech. 64, 357–364 (1994). https://doi.org/10.1007/BF00788407
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DOI: https://doi.org/10.1007/BF00788407