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Zeitschrift für Naturforschung A

A Journal of Physical Sciences

Editor-in-Chief: Holthaus, Martin

Editorial Board: Fetecau, Corina / Kiefer, Claus


IMPACT FACTOR 2017: 1.414

CiteScore 2018: 1.15

SCImago Journal Rank (SJR) 2018: 0.370
Source Normalized Impact per Paper (SNIP) 2018: 0.431

Online
ISSN
1865-7109
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Volume 46, Issue 6

Issues

Heteroclinic Bifurcations and Invariant Manifolds in Rocking Block Dynamics

B. Bruhn / B. P. Koch
Published Online: 2014-06-02 | DOI: https://doi.org/10.1515/zna-1991-0603

Abstract

A simple model of rigid block motion under the influence of external perturbations is discussed. For periodic forcings we prove the existence of Smale horseshoe chaos in the dynamics. For slender blocks a heteroclinic bifurcation condition is calculated exactly, i.e. without using perturbation methods. That means that our results are valid for arbitrary excitation amplitudes. Furthermore, analytical formulas for the first pieces of the stable and unstable manifolds are derived not only for periodically but also for transiently driven systems. In the case of small excitation and damping the Melnikov method is used to treat the full nonlinear problem

Keywords: Earthquake dynamics; Heteroclinic bifurcations; Melnikov method; Chaos

About the article

Received: 1991-02-13

Published Online: 2014-06-02

Published in Print: 1991-06-01


Citation Information: Zeitschrift für Naturforschung A, Volume 46, Issue 6, Pages 481–490, ISSN (Online) 1865-7109, ISSN (Print) 0932-0784, DOI: https://doi.org/10.1515/zna-1991-0603.

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© 1946 – 2014: Verlag der Zeitschrift für Naturforschung. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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