On New Modifications of Some Perturbation Procedures

Ismail, A. I.

doi:10.1155/2021/6681932

Cited by 2 publications

(1 citation statement)

References 12 publications

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“…It is assumed that the gyro has sufficiently small angular velocities about Ox and Oy axes, in addition to the restoring torque is large compared with the perturbed vector torque acting on the principal inertia gyro’s axes. Therefore, a large parameter ε≫1 35,36,37 can be inserted in the EOM and therefore, the AA 6,7,38 can be used to average the gyro’s system of motion, which can be to determine Euler’s angles. The geometric illustrations are given as a function of t and the body’s parameters.…”

Section: Description Of the Problemmentioning

confidence: 99%

Sufficiently small rotations of Lagrange’s gyro

Ismail

Amer

2023

Journal of Low Frequency Noise, Vibration and Active Control

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In this study, the motion of Lagrange’s gyro about its fixed point in the presence of a perturbed torque, a gyroscopic torque, and a varied restoring one is searched. We assume sufficiently small angular velocity components in the direction of the principal axes that differ from the dynamical symmetry one and a restoring torque that is considered to be greater than the perturbing one. In this manner, we replace the familiar small parameter that was used in previous works with a large one. In such cases, the gyro equations for motion (EOM) are formulated in the form of a two-degrees-of-freedom (DOF) autonomous system. We average the obtained system to get periodic solutions and motion’s geometric interpretation of the problem using the large parameter. The regular precession and the pure rotation of the motion are obtained. A numerical study is evaluated for asserted the used techniques and showed the influence of the changing parameters of motion on the gyro behavior. The trajectories of the motions and their stabilities are discussed and analyzed. The novelty of this work lies in how to adapt the method of large parameter (MLP) to solve the rigid body problem, especially since it has been assumed initially that its angular velocity or its initial energy are very small. MSC (2000): 70E20, 70E17, 70E15, 70E05

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Section: Description Of the Problemmentioning

confidence: 99%

Sufficiently small rotations of Lagrange’s gyro

Ismail

Amer

2023

Journal of Low Frequency Noise, Vibration and Active Control

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Chemical entropy generation and second-order slip condition on hydrodynamic Casson nanofluid flow embedded in a porous medium: a fast convergent method

Obalalu

2022

J Egypt Math Soc

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The chemical entropy generation analysis is an approach to optimize the performance of different thermal systems by investigating the related irreversibility of the system. The influences of second-order slip with the chemical reaction on the boundary layer flow and heat transfer of a non-Newtonian nanofluid in a non-Darcian porous medium have been investigated numerically. Simultaneous solutions are presented for first and second-order velocity slips. The second-order boundary conditions serve as a closure of a system of the continuity, transport, and energy differential equations. The current work differs from the previous studies in the application of a new second-order slip velocity model. The Casson fluid model is applied to characterize the non-Newtonian fluid behavior. The effect of the second slip parameter on the present physical parameters was discussed through graphs and it was found that this type of slip is a very important one to predict the investigated physical model. The present study provides two fast convergent methods on the semi-infinite interval, namely Chebyshev collocation method and optimal homotopy analysis method are used to analyze the fluid flow, heat, and mass transport. Compared with available analytical and numerical solutions, current methods are effective, quickly converging, and with great accuracy. It was shown that the account for the second-order terms in the boundary conditions noticeably affects the fluid flow characteristics and does not influence on the heat transfer characteristics.

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On New Modifications of Some Perturbation Procedures

Cited by 2 publications

References 12 publications

Sufficiently small rotations of Lagrange’s gyro

Sufficiently small rotations of Lagrange’s gyro

Chemical entropy generation and second-order slip condition on hydrodynamic Casson nanofluid flow embedded in a porous medium: a fast convergent method

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