Liapunov-Kozlov Method for Singular Cases

V. Čović; D. Djurić; M. Vesković; A. Obradović

doi:10.3879/j.issn.1000-0887.2011.09.012

Volume 32 Issue 9

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V. Čović, D. Djurić, M. Vesković, A. Obradović. Liapunov-Kozlov Method for Singular Cases[J]. Applied Mathematics and Mechanics, 2011, 32(9): 1127-1138. doi: 10.3879/j.issn.1000-0887.2011.09.012

Citation:

V. Čović, D. Djurić, M. Vesković, A. Obradović. Liapunov-Kozlov Method for Singular Cases[J]. Applied Mathematics and Mechanics, 2011, 32(9): 1127-1138. doi: 10.3879/j.issn.1000-0887.2011.09.012

Citation:

V. Čović, D. Djurić, M. Vesković, A. Obradović. Liapunov-Kozlov Method for Singular Cases[J]. Applied Mathematics and Mechanics, 2011, 32(9): 1127-1138. doi: 10.3879/j.issn.1000-0887.2011.09.012

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Liapunov-Kozlov Method for Singular Cases

doi: 10.3879/j.issn.1000-0887.2011.09.012

University of Belgrade, Faculty of Mechanical Engineering, Kraljice Marije 16, 11000 Belgrade, Serbia;
University of Kragujevac, Faculty of Mechanical Engineering, Dositejeva 19, 36000 Kraljevo, Serbia

Received Date: 2011-03-25
Rev Recd Date: 2011-06-15
Publish Date: 2011-09-15

Abstract

Abstract

Liapunov's first method,extended by V.Kozlov to nonlinear mechanical systems,was applied to the study of the instability of the position of equilibrium of a mechanical system moving in the field of conservative and dissipative forces.The cases with the tensor of inertia or the matrix of coefficients of the Rayleigh dissipative function singular in the equilibrium position were analyzed.This fact renders impossible the application of Liapunov's approach in the analysis of stability because in the equilibrium position the conditions of existence and uniqueness of solutions of differential equations of motion were not fulfilled.It was shown that Kozlov's generalization of Liapunov's first method was also applied in mentioned cases on condition that besides known one algebraic expression more was fulfilled.Three theorems on the instability of the equilibrium position were formulated.The results were illustrated by an example.
- instability,
- singular case,
- asymptotic motion,
- potential,
- dissipative force

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References(24)

References

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