{"publisher":"Birkhäuser Basel","publication":"Bifurcation and Chaos: Analysis, Algorithms, Applications","status":"public","year":"1991","doi":"10.1007/978-3-0348-7004-7_44","user_id":"55222","abstract":[{"text":"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.","lang":"eng"}],"publication_identifier":{"isbn":["978-3-0348-7006-1"]},"type":"book_chapter","_id":"8894","editor":[{"first_name":"R.","full_name":"Seydel, R.","last_name":"Seydel"},{"first_name":"F.W.","full_name":"Schneider, F.W.","last_name":"Schneider"},{"first_name":"T.","full_name":"Küpper, T.","last_name":"Küpper"},{"first_name":"H.","full_name":"Troger, H.","last_name":"Troger"}],"department":[{"_id":"151"}],"series_title":"International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / S{\\'e}rie Internationale d'Analyse Num{\\'e}rique","intvolume":"        97","date_updated":"2022-01-06T07:04:05Z","date_created":"2019-04-15T07:55:30Z","author":[{"first_name":"Peter","full_name":"Stelter, Peter","last_name":"Stelter"},{"id":"21220","first_name":"Walter","full_name":"Sextro, Walter","last_name":"Sextro"}],"citation":{"short":"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.","mla":"Stelter, Peter, and Walter Sextro. “Bifurcations in Dynamic Systems with Dry Friction.” <i>Bifurcation and Chaos: Analysis, Algorithms, Applications</i>, edited by R. Seydel et al., vol. 97, Birkhäuser Basel, 1991, pp. 343–47, doi:<a href=\"https://doi.org/10.1007/978-3-0348-7004-7_44\">10.1007/978-3-0348-7004-7_44</a>.","apa":"Stelter, P., &#38; Sextro, W. (1991). Bifurcations in Dynamic Systems with Dry Friction. In R. Seydel, F. W. Schneider, T. Küpper, &#38; H. Troger (Eds.), <i>Bifurcation and Chaos: Analysis, Algorithms, Applications</i> (Vol. 97, pp. 343–347). Birkhäuser Basel. <a href=\"https://doi.org/10.1007/978-3-0348-7004-7_44\">https://doi.org/10.1007/978-3-0348-7004-7_44</a>","bibtex":"@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={<a href=\"https://doi.org/10.1007/978-3-0348-7004-7_44\">10.1007/978-3-0348-7004-7_44</a>}, 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} }","ama":"Stelter P, Sextro W. Bifurcations in Dynamic Systems with Dry Friction. In: Seydel R, Schneider FW, Küpper T, Troger H, eds. <i>Bifurcation and Chaos: Analysis, Algorithms, Applications</i>. 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:<a href=\"https://doi.org/10.1007/978-3-0348-7004-7_44\">10.1007/978-3-0348-7004-7_44</a>","ieee":"P. Stelter and W. Sextro, “Bifurcations in Dynamic Systems with Dry Friction,” in <i>Bifurcation and Chaos: Analysis, Algorithms, Applications</i>, vol. 97, R. Seydel, F. W. Schneider, T. Küpper, and H. Troger, Eds. Birkhäuser Basel, 1991, pp. 343–347.","chicago":"Stelter, Peter, and Walter Sextro. “Bifurcations in Dynamic Systems with Dry Friction.” In <i>Bifurcation and Chaos: Analysis, Algorithms, Applications</i>, 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. <a href=\"https://doi.org/10.1007/978-3-0348-7004-7_44\">https://doi.org/10.1007/978-3-0348-7004-7_44</a>."},"page":"343-347","language":[{"iso":"eng"}],"volume":97,"title":"Bifurcations in Dynamic Systems with Dry Friction"}