Authors: Hedrih, Katica (Stevanović) 
Title: A trigger of coupled singularities
Journal: Meccanica
Volume: 38
Issue: 6
First page: 623
Last page: 642
Issue Date: 1-Jan-2003
Rank: M23
ISSN: 0025-6455
DOI: 10.1023/A:1025889628983
By using example of nonlinear dynamics of a pair of coupled gears, the phenomenon of appearance and disappearance of a trigger of coupled singularities and homoclinic orbits in the form of number 'eight' in the phase portrait in the phase plane is investigated. That phenomenon is an accompanying phenomenon of loss of stability of the local unique equilibrium position. For a generalized case under certain conditions, a theorem of the appearance of a trigger of coupled singularities in a nonlinear dynamical conservative system, the first derivative of the system potential energy which is a product of two periodic functions with different periods, and one bifurcation parameter, which is the cause for the appearance of new roots of these two functions, is defined.
Keywords: Conservative system | Homoclinic orbit | Nonlinear dynamics | Stability | Theorem on the existence of a trigger | Trigger of coupled singularities | Turbulent damping
Publisher: Springer Link
Project: Real Problems On Mechanics 

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