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On loss of stability of slow motions in stiff oscillatory systems
Author(s) -
Gusenkova Alla,
Steindl Alois,
Troger Hans
Publication year - 2004
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200410024
Subject(s) - spring (device) , pendulum , stability (learning theory) , motion (physics) , reduction (mathematics) , stiffness , double pendulum , control theory (sociology) , kapitza's pendulum , slow manifold , inverted pendulum , mechanics , classical mechanics , physics , mathematics , computer science , mathematical analysis , geometry , thermodynamics , nonlinear system , singular perturbation , control (management) , quantum mechanics , machine learning , artificial intelligence
In stiff oscillatory systems often a reduction of the order of the system is possible by splitting the motion into an essential motion on a nearby slow manifold and neglecting the fast motion. However, if the system is conservative the question of stability of the slow motion is a delicate problem. For various spring pendulum systems we, first, perform numerical simulations showing that if the stiffness of the springs is gradually reduced the slow motion looses stability. For a single spring pendulum we give an explanation of this loss of stability. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)