The asymptotic solutions of the governing system of a charged symmetric body under the influence of external torques

Galal, A. A.; Amer, T. S.; Elkafly, H.F.; Amer, W. S.

doi:10.1016/j.rinp.2020.103160

Cited by 26 publications

(19 citation statements)

References 28 publications

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“…To check the stability of the system, [46][47][48] we need to obtain the solvability conditions and the modification equations for the acquired solutions. Therefore, we will examine the two cases of the primary external resonance that occurs simultaneously, that is, we consider a combination of p 1 ≈ 1 and p 2 ≈ ω which describes the nearness of p 1 and p 2 to 1 and ω, respectively.…”

Section: Resonance Cases and Stability's Evaluationmentioning

confidence: 99%

Controlling the kinematics of a spring-pendulum system using an energy harvesting device

Amer

Tian

et al. 2022

Journal of Low Frequency Noise, Vibration and Active Control

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This work focuses on vibration alleviation and energy harvesting in a dynamical system of a spring-pendulum. The structure of the pendulum is modified using an independent electromagnetic harvesting system. The harvesting depends on the oscillation of a magnet in a coil. An endeavor has been made to get both the energy harvesting and mitigation of vibration efficacy of the harvester. The governing kinematics equations are derived using Lagrange’s equations and are solved asymptotically using the multiple scales method to achieve the intended outcome as new and precise results. The resonance states are classified, and the influence of various parameters of the studied system is analyzed. Fixed points at steady states are categorized into stable and unstable. The time behavior of the solutions, the modified amplitudes, and phases are examined and interpreted in the light of their graphical plots. Zones of stability and instability are concerned, in which the system’s behavior is stable for a wide range of used parameters. This model has become essential in recent times as it uses control sensors in industrial applications, buildings, infrastructure, automobiles, and transportation.

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Section: Resonance Cases and Stability's Evaluationmentioning

confidence: 99%

Controlling the kinematics of a spring-pendulum system using an energy harvesting device

Amer

Tian

et al. 2022

Journal of Low Frequency Noise, Vibration and Active Control

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“…The constants ðM i ; i ¼ 1; 2; 3Þ will be determined later. Due to the generated solutions (19), we assume the required analytical periodic general solutions in the forms…”

Section: Constructing the Analytic Periodic Solutionsmentioning

confidence: 99%

“…Different analytic solutions for the rigid motions are obtained in Refs. 14–19 using the aforementioned methods when the influence of a gyrostatic moment is considered. In Ref.…”

Section: Introductionmentioning

confidence: 99%

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A slow rotary dynamic motion of a disc under the influence of torque with the concept of a large parameter

Ismail

Abdulaziz

2022

Journal of Low Frequency Noise, Vibration and Active Control

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A rotary motion is studied, which is used as a paradigm in both mathematics and dynamics. In this motion, the body moves around its axis. Important examples of this motion are the earth, wheels for cars or bicycles, cooling fans, airplanes, radars, and motion of the discs. In this article, we consider one of these motions such as the slow rotational motion of a disc of high natural frequency around a fixed point different from its center of mass. Suppose a constant gyrostatic couple acts on the body about the axis of symmetry. Let us consider the axis of symmetry coincide with one of the main axes of inertia. The controlled nonlinear independent system of equations of motion is obtained in the form of six nonlinear differential equations in the presence of three independent first integrals. This system is reduced to an alternative independent quasi-linear system consisting of two differential equations with only one integral. At first, when the body rotates slowly with a small angular speed about the axis of the symmetry, we achieve a large parameter for the motion which is proportional to the inverse of the angular velocity component. Then, we use the large parameter technique to obtain approximate and high-frequency analytic solutions for this motion. This technique enables us to introduce new conditions of the motion, save a lot of energy required to move the disc, and obtain new approximated solutions in a new domain of the disc parameters. We present a digital example of the problem to clarify the inferences of the motion depending on the parameters of the body. On the other hand, we use the Runge–Kutta algorithmic method to obtain the numerical solutions corresponding to the approximate solutions of the considered independent system. We investigate the inaccuracies and errors of analytic and numerical solutions by comparing them. This problem offers many applications in gyroscope dynamics, industrial engineering, astrophysics, navigation, satellites, and space engineering.

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“…One of the significant issues in applications in assorted branches of science such as physics and astronomy is the problem of a rigid body and its extension to a gyrostat (see, e.g., [21][22][23]). So, it is a beneficial model for research from different points of view [24][25][26][27][28][29]. Consequently, the present work interested in analyzing the general motion of a rigid body about its fixed point that happens under the effect of a combination of potential (velocity-independent) forces and gyroscopic (velocity-dependent) forces.…”

Section: Introductionmentioning

confidence: 99%

Quartic Integral in Rigid Body-Gyrostat Dynamics

Mnasri

Elmandouh

2020

Advances in Astronomy

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In this work, we investigate the problem of constructing new integrable problems in the dynamics of the rigid body rotating about its fixed point as results of the effect of a combination of potential and gyroscopic forces possessing a common symmetry axis. We introduce two new integrable problems in a rigid body dynamics that generalize some integrable problems in this field, known by names of Chaplygin and Yehia–Elmandouh.

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The asymptotic solutions of the governing system of a charged symmetric body under the influence of external torques

Cited by 26 publications

References 28 publications

Controlling the kinematics of a spring-pendulum system using an energy harvesting device

Controlling the kinematics of a spring-pendulum system using an energy harvesting device

A slow rotary dynamic motion of a disc under the influence of torque with the concept of a large parameter

Quartic Integral in Rigid Body-Gyrostat Dynamics

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