by Peter Stelter, Walter Sextro
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.
Reference:
Stelter, P.; Sextro, W.: Bifurcations in Dynamic Systems with Dry Friction. Chapter in Bifurcation and Chaos: Analysis, Algorithms, Applications (R. Seydel, F.W. Schneider, T. Küpper, H. Troger, eds.), Birkhäuser Basel, volume 97, 1991.
Bibtex Entry:
@INCOLLECTION{Stelter1991,
author = {Stelter, Peter and Sextro, Walter},
title = {Bifurcations in Dynamic Systems with Dry Friction},
booktitle = {Bifurcation and Chaos: Analysis, Algorithms, Applications},
publisher = {Birkh{\"a}user Basel},
year = {1991},
editor = {Seydel, R. and Schneider, F.W. and K{\"u}pper, T. and Troger, H.},
volume = {97},
series = {International Series of Numerical Mathematics / Internationale Schriftenreihe
zur Numerischen Mathematik / S{\'e}rie Internationale d'Analyse Num{\'e}rique},
pages = {343-347},
__markedentry = {[K. Agbons jr:6]},
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.},
bdsk-url-1 = {http://dx.doi.org/10.1007/978-3-0348-7004-7_44},
doi = {10.1007/978-3-0348-7004-7_44},
isbn = {978-3-0348-7006-1},
language = {English},
owner = {K. Agbons jr},
timestamp = {2013.11.23},
url = {http://dx.doi.org/10.1007/978-3-0348-7004-7_44}
}