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 Nelin. Dinam., 2015, Volume 11, Number 1, Pages 127–146 (Mi nd469)

On the equilibrium position stability of discrete model of filling hose under the action of reactive force

Alexander E. Baikov, Andrey Yu. Mayorov

Moscow Aviation Institute (National Research University), Volokolamskoe Shosse, 4, GSP-3, A-80, Moscow, 125993, Russia

Abstract: The destabilization of the stable equilibrium position of a non-conservative system with three degrees of freedom under the action of a linear viscous friction force is considered. The dissipation is assumed to be completed. The standard methods of the stability theory are using for solving problem. Stability of equilibrium position is studied in the linear approximation. The coefficients of characteristic polynomial are constructed by using Le Verrier's algorithm. Ziegler's effect condition and criterion for the stability are constructed by using perturbation theory. Stability of the three-link rod system's equilibrium position is investigated, when there is no dissipative force. Ziegler's area and criterion for the stability of the equilibrium position of a system with three degrees of freedom, in which the friction forces take small values, are constructed. The influence of large friction forces is investigated. The results of the study may be used for the analysis of stability of a non-conservative system with three degrees of freedom. Also, the three-link rod system may be used as discrete model of filling hose under the action of reactive force.

Keywords: fillling hose, discrete model, three-link rod system, tracking force, dissipative forces, asymptotically stability, Ziegler’s effect, Ziegler’s areas, criterion for the stability.

 Funding Agency Grant Number Russian Science Foundation 14-21-00068

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UDC: 531.01
MSC: 70E50
Revised: 28.01.2015

Citation: Alexander E. Baikov, Andrey Yu. Mayorov, “On the equilibrium position stability of discrete model of filling hose under the action of reactive force”, Nelin. Dinam., 11:1 (2015), 127–146

Citation in format AMSBIB
\Bibitem{BaiMay15} \by Alexander~E.~Baikov, Andrey~Yu.~Mayorov \paper On the equilibrium position stability of discrete model of filling hose under the action of reactive force \jour Nelin. Dinam. \yr 2015 \vol 11 \issue 1 \pages 127--146 \mathnet{http://mi.mathnet.ru/nd469} \elib{https://elibrary.ru/item.asp?id=23051493} 

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This publication is cited in the following articles:
1. A. Yu. Maiorov, “O destabilizatsii polozheniya ravnovesiya, vyzvannoi lineinymi i kvadratichnymi silami vyazkogo treniya”, Zhurnal SVMO, 18:3 (2016), 49–60
2. P. S. Krasil'nikov, A. Yu. Maiorov, “On the stability of equilibrium of a mechanical system with tracking, potential, and small dissipative forces”, Mech. Sol., 53:2 (2018), S52–S59
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