On loss of stability of slow motions in stiff oscillatory systems | Zendy

Gusenkova Alla | Zendy; Steindl Alois | Zendy; Troger Hans | Zendy

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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)

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