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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Author
Stelter, Peter;
Sextro, WalterLibreCat
Book Editor
Seydel, R.;
Schneider, F.W.;
Küpper, T.;
Troger, H.
Department
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.
Publishing Year
Book Title
Bifurcation and Chaos: Analysis, Algorithms, Applications
Series Title / Volume
International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / S{\'e}rie Internationale d'Analyse Num{\'e}rique
Volume
97
Page
343-347
ISBN
LibreCat-ID
Cite this
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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