On the existence of new integrable cases for Euler-Poisson equations in Newtonian fields

El-Borhamy, Mohamed

doi:10.1016/j.aej.2019.06.004

Cited by 8 publications

(9 citation statements)

References 17 publications

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“…If the system has no damping ( = ) Q 0 , according to Hamilton-Jacobi's equations [10,20] and using Charpit's equations, the following particular solution can be deduced:…”

Section: Modeling Systemmentioning

confidence: 99%

Floquet analysis of linear dynamic RLC circuits

2020

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AbstractIn this article, the linear dynamic analysis of AC generators modeled as RLC circuits with periodically time-varying inductances via Floquet’s theory is considered. Necessary conditions for the dynamic stability are derived. The harmonic balance method is employed to predict the transition curves and stability domains. An approximate expression for the Floquet form of solution is constructed using Whittaker’s method in the neighborhood of transition curves. Numerical verifications for the obtained theoretical results are considered. In accordance with the experimental results, a satisfactory agreement is relatively achieved with the closed experimental literature of the problem.

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“…If the system has no damping ( = ) Q 0 , according to Hamilton-Jacobi's equations [10,20] and using Charpit's equations, the following particular solution can be deduced:…”

Section: Modeling Systemmentioning

confidence: 99%

Floquet analysis of linear dynamic RLC circuits

2020

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“…In general, the energy conservation principles of dynamical systems have been proposed for the modeling of the law of motion of certain grown phenomena in physical sciences, cf. [28][29][30][31][32][33], so that the law of motion of capital occurs with a fractional time rate of energy and exhibiting whenever the system behavior is dependent at least in part on its history. e principle of energy conservation implies…”

Section: Fractional Delayed Bfds Modelmentioning

confidence: 99%

Chaos Prediction in Fractional Delayed Energy‐Based Models of Capital Accumulation

2021

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This paper presents the nonlinear dynamic analysis of energy-based models arisen from the applied systems characterized by the energy transport in the presence of fractional order derivative and time delay. The studied model is the fractional version of Bianca-Ferrara-Dalgaard-Strulik (BFDS) model of economy which is viewed as a transport network for energy in which the law of motion of capital occurs. By considering the time delay as bifurcation parameter, a proof to investigate the existence of Hopf bifurcation and the phase lock solutions using the Poincare-Linstedt and the harmonic balance methods is given. At definite values of time delay, period-doubling bifurcations followed up by the consequences of chaotic states are detected. Simulation results assure that the BFDS model can generate new (hyper) chaotic attractors beyond half order derivatives through the effect of the time delay on that system. In accordance with the literatures related to the problem of chaos, the concluded results confirm the proposed theorem by El-Borhamy in which the time delay possesses the ability to change the dynamic state of nonlinear systems from regular to chaotic within the fractional order derivative domain.

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“…Several techniques are used to predict the stability of systems, cf. [42][43][44][45][46][47]. Based on the constructed semi-analytical solutions, it is readily to apply the energy-rate method to obtain three dimensional illustration of stability surface showing a sense of relative stability of parameter plane, cf.…”

Section: Construction Of Stability Domainsmentioning

confidence: 99%

Modeling and Semi-Analytic Stability Analysis for Dynamics of AC Machines

et al. 2021

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In this article, a semi-analytical technique is proposed to predict stable sustained periodic responses of AC electrical machines. Based on such desired outputs, the proper selections of machine variables are captured, such as the perturbation parameter arisen from the relative movement between the stationary and rotating parts. Compared to the experimental results, the derived analytical results are relatively well-fitted with the studied practical cases.

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On the existence of new integrable cases for Euler-Poisson equations in Newtonian fields

Cited by 8 publications

References 17 publications

Floquet analysis of linear dynamic RLC circuits

Floquet analysis of linear dynamic RLC circuits

Chaos Prediction in Fractional Delayed Energy‐Based Models of Capital Accumulation

Modeling and Semi-Analytic Stability Analysis for Dynamics of AC Machines

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