Titlebook: Nonlinear Dynamics of Discrete and Continuous Systems; Andrei K. Abramian,Igor V. Andrianov,Valery A. Gai Book 2021 Springer Nature Switze

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Expanding the Applicability of the Competitive Modes Conjecture,g Resonance Theory. Up till now, the Conjecture has only been used to study multipolynomial systems because of their simplicity. As such, the study of non-multipolynomial systems is sparse, filled with ambiguity, and lacks mathematical structure. This paper strives to rectify this dilemma, providing

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,The Construction of Stabilizing Regulators Sets for Nonlinear Control Systems with the Help of Padéstate dependent coefficients (SDC) systems are considered. The conditions for the existence of approximate symbolic constructions describing the sets of stabilizing regulators based on the asymptotic expansions of the solutions of the matrix Riccati equations arising in the optimal control theory ar

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,Galerkin’s Method was not Developed by Ritz, Contrary to the Timoshenko’s Statement,o to Grigolyuk. B. G. Galerkin (1871–1945) is the author of the first letter to S. P. Timoshenko. Second letter to him is by E. I. Grigolyuk. The letters are concerned with the method known as the Galerkin method (in the West), or the Bubnov-Galerkin method or the Bubnov method (in Russia). The lett

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Free Generalized van der Pol Oscillators: Overview of the Properties of Oscillatory Responses,with the powers that can be any positive real numbers, while the restoring force is either linear or purely nonlinear. The cases of small and large values of the damping parameter are considered. In the former case, an overview of contributions related to the amplitude and frequency of free limit cy

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Theoretical Determination of the Five Physical Constants of the Toupin-Mindlin Gradient Elasticity t is shown that the elastic energy density of the polycrystalline medium depends non-locally on the non-uniform field of average deformations. In the case of smooth fields of average deformations it could be considered that the energy density locally depends not only on the values of deformations, b

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A Parametrically Excited Nonlinear Wave Equation,square we find an infinite number of 1 : 1 resonances and in addition accidental resonances. Using Galerkin projection on 2 modes in 1 : 1 resonance we find stable normal mode periodic solutions and unstable periodic solutions in general position; the location in phase-space is characterised as a tr