Averaging method for the stability analysis of strongly nonlinear mechanical systems

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Averaging method for the stability analysis of strongly nonlinear mechanical systems. / Александров, Александр Юрьевич; Efimov, Denis V.

In: Automatica, Vol. 146, 110576, 12.2022.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{93d17bb7183a4433ab3ec4a35020476b,

title = "Averaging method for the stability analysis of strongly nonlinear mechanical systems",

abstract = "A mechanical system under strongly nonlinear potential and dissipative forces, with nonlinear nonstationary perturbations having zero mean values, is studied. Proposing a special construction of Lyapunov function, the conditions are found, under which the perturbations do not influence the asymptotic stability of the trivial equilibrium position of the system. These conditions include the requirements on asymptotic stability of the disturbance-free system and the relations of the nonlinearity orders between potential and dissipative forces. The developed approach is extended to the problem of monoaxial stabilization of a rigid body.",

keywords = "Asymptotic stability, Averaging, Lyapunov function, Nonlinear mechanical system, Nonstationary perturbations",

author = "Александров, {Александр Юрьевич} and Efimov, {Denis V.}",

note = "Publisher Copyright: {\textcopyright} 2022 Elsevier Ltd",

year = "2022",

month = dec,

doi = "10.1016/j.automatica.2022.110576",

language = "English",

volume = "146",

journal = "Automatica",

issn = "0005-1098",

publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Averaging method for the stability analysis of strongly nonlinear mechanical systems

AU - Александров, Александр Юрьевич

AU - Efimov, Denis V.

PY - 2022/12

Y1 - 2022/12

N2 - A mechanical system under strongly nonlinear potential and dissipative forces, with nonlinear nonstationary perturbations having zero mean values, is studied. Proposing a special construction of Lyapunov function, the conditions are found, under which the perturbations do not influence the asymptotic stability of the trivial equilibrium position of the system. These conditions include the requirements on asymptotic stability of the disturbance-free system and the relations of the nonlinearity orders between potential and dissipative forces. The developed approach is extended to the problem of monoaxial stabilization of a rigid body.

AB - A mechanical system under strongly nonlinear potential and dissipative forces, with nonlinear nonstationary perturbations having zero mean values, is studied. Proposing a special construction of Lyapunov function, the conditions are found, under which the perturbations do not influence the asymptotic stability of the trivial equilibrium position of the system. These conditions include the requirements on asymptotic stability of the disturbance-free system and the relations of the nonlinearity orders between potential and dissipative forces. The developed approach is extended to the problem of monoaxial stabilization of a rigid body.

KW - Asymptotic stability

KW - Averaging

KW - Lyapunov function

KW - Nonlinear mechanical system

KW - Nonstationary perturbations

UR - http://www.scopus.com/inward/record.url?scp=85137620428&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/5145ebee-6a4e-3a2c-b1d7-1105d9b3eac7/

U2 - 10.1016/j.automatica.2022.110576

DO - 10.1016/j.automatica.2022.110576

M3 - Article

VL - 146

JO - Automatica

JF - Automatica

SN - 0005-1098

M1 - 110576

ER -

ID: 99950892