Ahmed Hassan Elneklawy
@kfs.edu.eg
Kafrelsheikh university/ Faculty of science/ Mathematics department
lecturer
RESEARCH, TEACHING, or OTHER INTERESTS
Applied Mathematics, Mathematical Physics, Modeling and Simulation, Numerical Analysis
Scopus Publications
Scholar Citations
Scholar h-index
Scopus Publications
T. S. Amer, H. F. El-Kafly, A. H. Elneklawy, and A. A. Galal
Springer Science and Business Media LLC
AbstractThis study explores the dynamical rotary motion of a charged axisymmetric spinning rigid body (RB) under the effect of a gyrostatic moment (GM). The influence of transverse and invariable body fixed torques (IBFTs), and an electromagnetic force field, is also considered. Euler’s equations of motion (EOM) are utilized to derive the regulating system of motion for the problem in a suitable formulation. Due to the lack of torque exerted along the spin axis and the nearly symmetrical nature of the RB, the spin rate is nearly unchanged. Assuming slight angular deviations of the spin axis relative to a fixed direction in space, it is possible to derive approximate analytical solutions (AS) in closed form for the attitude, translational, and rotational movements. These concise solutions that are expressed in complex form are highly effective in analyzing the maneuvers performed by spinning RBs. The study focuses on deriving the AS for various variables including angular velocities, Euler’s angles, angular momentum, transverse displacements, transverse velocities, axial displacement, and axial velocity. The graphical simulation of the subsequently obtained solutions is presented to show their precision. Furthermore, the positive impacts that alterations in the body’s parameters have on the motion’s behavior are presented graphically. The corresponding phase plane curves, highlighting the influence of different values in relation to the electromagnetic force field, the GM, and the IBFTs are drawn to analyze the stability of the body’s motion. This study has a significant role in various scientific and engineering disciplines. Its importance lies in its ability to optimize mechanical systems, explain celestial motion, and enhance spacecraft performance.
T. S. Amer, H. F. El-Kafly, A. H. Elneklawy, and A. A. Galal
Springer Science and Business Media LLC
AbstractThis paper aims to explore the rotatory spatial motion of an asymmetric rigid body (RB) under constant body-fixed torques and a nonzero first component gyrostatic moment vector (GM). Euler's equations of motion are used to derive a set of dimensionless equations of motion, which are then proposed for the stability analysis of equilibrium points. Specifically, this study develops 3D phase space trajectories for three distinct scenarios; two of them are applied constant torques that are directed on the minor and major axes, while the third one is the action of applied constant torque on the body’s middle axis. Novel analytical and simulation results for both scenarios of constant torque applied along the minor and middle axes are provided in the context of separatrix surfaces, equilibrium manifolds, periodic or non-periodic solutions, and periodic solutions’ extreme. Concerning the scenario of a directed torque on the major axis, a numerical solution for the problem is presented in addition to a simulation of the graphed results for the angular velocities' trajectories in various regions. Moreover, the influence of GM is examined for each case and a full modeling for the body's stability has been present. The exceptional impact of these results is evident in the development and assessment of systems involving asymmetric RBs, such as satellites and spacecraft. It may serve as a motivating factor to explore different angles within the GM in similar cases, thereby influencing various industries, including engineering and astrophysics applications.
A. A. Galal, T. S. Amer, A. H. Elneklawy, and H. F. El-Kafly
Springer Science and Business Media LLC
AbstractThe rotational motion of a charged rigid body (RB) is examined. The RB has a spherical cavity that contains an incompressible viscous liquid. The influence of a gyrostatic moment (GM), constant torques at the body-connected axes, and the action of the torque of a resistant force, due to the shape of the liquid, are considered. Assuming the liquid has a sufficiently high velocity, the Reynolds number does indeed have a small value. The regulating system of motion is derived in an appropriate formulation through Euler's equations of motion. The averaging method is used to approach a suitable form of the motion's governing system. In addition to using Taylor’s method to reach a solution for the averaged equations of motion of the RB, some initial conditions are considered to approach the required results. The asymptotic approach of the averaged system besides the numerical analysis enables us to obtain the appropriate results of the problem. To draw attention to the beneficial effects of the different values of the body’s parameter on the motion's behavior, these results are graphed through a computer program along with the associated phase plane curves. These diagrams illustrate the influence of several values respected to the GM, charge, body-constant torques, and resistive force torque. The stability of the RB's motion has also been discussed through the represented phase plane diagrams. These results are viewed as a generalization of prior ones, which have been reported for the scenario of an uncharged body or the absence case of the GM. The significance of the obtained results is due to its numerous real-world applications in life, such as for spaceships and wagons carrying liquid fuel.