Bifurcations in Dynamic Systems with Dry Friction

P. Stelter, W. Sextro, in: R. Seydel, F.W. Schneider, T. Küpper, H. Troger (Eds.), Bifurcation and Chaos: Analysis, Algorithms, Applications, Birkhäuser Basel, 1991, pp. 343–347.

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Abstract
Dry friction is a main factor of self-sustained oscillations in dynamic systems. The mathematical modelling of dry friction forces result in strong nonlinear equations of motion. The bifurcation behaviour of a deterministic system has been investigated by the bifurcation theory. The stability of stationary solutions has been analyzed by the eigenvalues of the Jacobian. Period doublings and Hopf-bifurcations as well as turning points could be determined with the program package BIFPACK. Phase plane plots of periodic and chaotic motions have been shown for a better understanding of the bifurcation diagrams. Both, unstable branches and stable coexisting solutions have been calculated. Several jumping effects, which are typical for nonlinear systems, have been found.
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Book Title
Bifurcation and Chaos: Analysis, Algorithms, Applications
Volume
97
Page
343-347
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Stelter P, Sextro W. Bifurcations in Dynamic Systems with Dry Friction. In: Seydel R, Schneider FW, Küpper T, Troger H, eds. Bifurcation and Chaos: Analysis, Algorithms, Applications. Vol 97. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / S{\’e}rie Internationale d’Analyse Num{\’e}rique. Birkhäuser Basel; 1991:343-347. doi:10.1007/978-3-0348-7004-7_44
Stelter, P., & Sextro, W. (1991). Bifurcations in Dynamic Systems with Dry Friction. In R. Seydel, F. W. Schneider, T. Küpper, & H. Troger (Eds.), Bifurcation and Chaos: Analysis, Algorithms, Applications (Vol. 97, pp. 343–347). Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7004-7_44
@inbook{Stelter_Sextro_1991, series={International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / S{\’e}rie Internationale d’Analyse Num{\’e}rique}, title={Bifurcations in Dynamic Systems with Dry Friction}, volume={97}, DOI={10.1007/978-3-0348-7004-7_44}, booktitle={Bifurcation and Chaos: Analysis, Algorithms, Applications}, publisher={Birkhäuser Basel}, author={Stelter, Peter and Sextro, Walter}, editor={Seydel, R. and Schneider, F.W. and Küpper, T. and Troger, H.Editors}, year={1991}, pages={343–347}, collection={International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / S{\’e}rie Internationale d’Analyse Num{\’e}rique} }
Stelter, Peter, and Walter Sextro. “Bifurcations in Dynamic Systems with Dry Friction.” In Bifurcation and Chaos: Analysis, Algorithms, Applications, edited by R. Seydel, F.W. Schneider, T. Küpper, and H. Troger, 97:343–47. International Series of Numerical Mathematics / Internationale Schriftenreihe Zur Numerischen Mathematik / S{\’e}rie Internationale d’Analyse Num{\’e}rique. Birkhäuser Basel, 1991. https://doi.org/10.1007/978-3-0348-7004-7_44.
P. Stelter and W. Sextro, “Bifurcations in Dynamic Systems with Dry Friction,” in Bifurcation and Chaos: Analysis, Algorithms, Applications, vol. 97, R. Seydel, F. W. Schneider, T. Küpper, and H. Troger, Eds. Birkhäuser Basel, 1991, pp. 343–347.
Stelter, Peter, and Walter Sextro. “Bifurcations in Dynamic Systems with Dry Friction.” Bifurcation and Chaos: Analysis, Algorithms, Applications, edited by R. Seydel et al., vol. 97, Birkhäuser Basel, 1991, pp. 343–47, doi:10.1007/978-3-0348-7004-7_44.

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