The period on a family of non-linear oscillations and periodic motions of a perturbed system at a critical point of the family

Тхай, В. Н.

doi:10.1016/j.jappmathmech.2010.11.007

Cited by 6 publications

(9 citation statements)

References 4 publications

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“…1, the family starts out as an equilibrium and adjoins the separatrix. By a direct calculation, as was done previously, 21 we see that the period is the strictly increasing function h. Therefore, 11,21 we have a non-degenerate case for the SPM.…”

Section: The Asymmetrical Oscillations Of a Satellitementioning

confidence: 57%

Periodic motions of a perturbed reversible mechanical system

Тхай¹

2015

Journal of Applied Mathematics and Mechanics

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Section: The Asymmetrical Oscillations Of a Satellitementioning

confidence: 57%

Periodic motions of a perturbed reversible mechanical system

Тхай¹

2015

Journal of Applied Mathematics and Mechanics

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“…periodic solutions. Since subsystems are autonomous, we have isochronous single-frequency oscillations in the linear model, while in the nonlinear model in the non-degenerate case there is an alternative: either a cycle or a family of periodic solutions with the period depending on a single parameter [10] is realized (i.e. the law [11][12][13] called critical (c-point).…”

Section: The Model Containing Coupled Subsystems (Mccs)mentioning

confidence: 99%

“…. , m, and the non-degenerate case [10] is realized for the periodic solution. Then subsystems have only o-points, such that the MCCS is functioning in the main oscillations mode.…”

Section: Mccs Of Class Amentioning

confidence: 99%

“…On the one hand, (5) gives necessary conditions for 2π-periodic solutions of (1). On the other hand, (5) To prove Theorem 1 [10] we use the implicit function theorem, which is applied to find necessary and sufficient conditions of a periodic solution. Since subsystems have o-points, the system of m equations that represents conditions of periodic solution coinsides with amplitude equations (5).…”

Section: Mccs Of Class Amentioning

confidence: 99%

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On the model containing coupled subsystems

Тхай¹,

Barabanov²

2014

Sci Publ State Univ Novi Pazar Ser A

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Abstract:The model containing coupled subsystems (MCCS), which decouples into independent subsystems as the coupling vanishes, is considered. The subsystems of the MCCS are described by autonomous systems of ordinary differential equations. Each subsystem is supposed to admit a single parameter family of periodic motions. The general characteristics of the MCCS are presented. Some problems concerning the MCCS are stated, i.e. the problems of oscillations existence, bifurcations, stability, stabilization, and resonance. The classification of MCCS is proposed, the currently investigated classes of MCCS are announced. One class of MCCS is studied in detail, the corresponding results are presented.

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“…It turned out [2,3] that the period on the family of symmetric oscillations of the invertible mechanical system depends only on a single parameter c, though the dimensionality of the family Σ(h) can exceed one. This fact takes place also in the autonomous system of general differential Eqs.…”

Section: Introductionmentioning

confidence: 99%

Quasiautonomous system: Oscillations, stability, and stabilization at the ordinary point of the family of periodic solutions

Barabanov

Тхай

2013

Autom Remote Control

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Consideration was given to the single-frequency oscillations of the periodic system allied to the nonlinear multidimensional autonomous system. It was assumed that the generating autonomous system admits a family of solutions with period depending on a single parameter: all points of the family break down into the ordinary points whose derivative of the period with respect to the parameter is other than zero and the critical points where this derivative vanishes. Generation of oscillations and their stability at the ordinary point of the family were studied. These problems were solved earlier for the second-order system.

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The period on a family of non-linear oscillations and periodic motions of a perturbed system at a critical point of the family

Cited by 6 publications

References 4 publications

Periodic motions of a perturbed reversible mechanical system

Periodic motions of a perturbed reversible mechanical system

On the model containing coupled subsystems

Quasiautonomous system: Oscillations, stability, and stabilization at the ordinary point of the family of periodic solutions

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