Please use this identifier to cite or link to this item: https://scidar.kg.ac.rs/handle/123456789/9959
Title: Lyapunov-Kozlov method for singular cases
Authors: Čović V.
Djuric D.
Vesković, Miroslav
Obradovic, Aleksandar
Issue Date: 2011
Abstract: Lyapunov's first method, extended by Kozlov to nonlinear mechanical systems, is applied to study the instability of the equilibrium position of a mechanical system moving in the field of conservative and dissipative forces. The cases with a tensor of inertia or a matrix of coefficients of the Rayleigh dissipative function are analyzed singularly in the equilibrium position. This fact renders the impossible application of Lyapunov's approach in the analysis of the stability because, in the equilibrium position, the conditions of the existence and uniqueness of the solutions to the differential equations of motion are not fulfilled. It is shown that Kozlov's generalization of Lyapunov's first method can also be applied in the mentioned cases on the conditions that, besides the known algebraic expression, more are fulfilled. Three theorems on the instability of the equilibrium position are formulated. The results are illustrated by an example. © 2011 Shanghai University and Springer-Verlag Berlin Heidelberg.
URI: https://scidar.kg.ac.rs/handle/123456789/9959
Type: article
DOI: 10.1007/s10483-011-1494-6
ISSN: 0253-4827
SCOPUS: 2-s2.0-80052599047
Appears in Collections:Faculty of Mechanical and Civil Engineering, Kraljevo

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