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	STABILITY OF NONLINEAR DYNAMICAL SYSTEM MOTION UNDER CONSTANTLY ACTING PERTURBATIONS</div>

Gennady I Melnikov, Melnikov Vitaly G, Dudarenko Natalya Alexandrovna, Vladislav V. Talapov

doi:10.17586/2226-1494-2019-19-2-216-221

2019 , VOLUME 19, NUMBER 2 ( MARCH–APRIL )

ISSN 2226-1494 (print), ISSN 2500-0373 (online)

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Nikiforov
Vladimir O.
D.Sc., Prof.

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doi: 10.17586/2226-1494-2019-19-2-216-221

STABILITY OF NONLINEAR DYNAMICAL SYSTEM MOTION UNDER CONSTANTLY ACTING PERTURBATIONS

G. I. Melnikov, V. G. Melnikov, N. A. Dudarenko, V. V. Talapov

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Article in Russian

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Melnikov G.I., Melnikov V.G., Dudarenko N.A., Talapov V.V. Stability of nonlinear dynamical system motion under constantly acting perturbations. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2019, vol. 19, no. 2, pp. 216–221 (in Russian). doi: 10.17586/2226-1494-2019-19-2-216-221

Abstract

We consider the motion of a mechanical system with several degrees of freedom near zero of the phase space of states under conditions of constantly acting small perturbations. The generalized forces are represented in the dynamic equations by homogeneous forms of the first and the third degree with respect to the phase coordinates and by small time functions characterizing the constantly acting perturbations. It is assumed that there are no multiple eigenvalues of the matrix of the system linear part. For a definitely positive quadratic Lyapunov function, we define a differential inequality with Riccati differential comparison equation, together with an exponential differential inequality that is integrable in quadratures. When solving Riccati quadratic differential inequality, we assume one particular solution of Riccati equation to be known. As a result of integrating in quadratures of the exponential differential inequalities, the estimate of transient processes in the finite domain of the phase coordinates is obtained.

Keywords: mechanical system, dynamical system, generalized and phase coordinates, motion stability, Lyapunov functions, differential equation of comparison, exponential differential inequality, transient process functional estimates

Acknowledgements. This work was supported by the RFBR Grant 16-08-00997, 17-01-00672.

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