Analyzing the spatial motion of a rigid body subjected to constant body-fixed torques and gyrostatic moment

Amer, T. S.; El-Kafly, H. F.; Elneklawy, A. H.; Galal, A. A.

doi:10.1038/s41598-024-55964-z

Cited by 5 publications

(1 citation statement)

References 26 publications

(26 reference statements)

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“…In Ref. 23 , the authors’ goal was to investigate the rotational movement of an asymmetric RB subjected to IBFTs and a non-zero first component GM. They employed Euler’s EOMs to derive a series of dimensionless equations, which were then suggested for analyzing the stability of equilibrium points.…”

Section: Introductionmentioning

confidence: 99%

Analyzing the dynamics of a charged rotating rigid body under constant torques

Amer,

El-Kafly,

Elneklawy

et al. 2024

Sci Rep

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This 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.

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Section: Introductionmentioning

confidence: 99%

Analyzing the dynamics of a charged rotating rigid body under constant torques

Amer,

El-Kafly,

Elneklawy

et al. 2024

Sci Rep

Self Cite

View full text Add to dashboard Cite

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The asymptotic solutions for the motion of a charged symmetric gyrostat in the irrational frequency case

Amer,

Abady,

Abdo

et al. 2024

Sci Rep

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The primary objective of this study is to explore the spatial rotary movements of a symmetrically charged rigid body (RB) that is rotating around a fixed point, akin to Lagrange’s scenario as a novel scenario where its center of mass experiences a slight displacement from the symmetry dynamic axis. The body’s movement is presumed to be affected by a gyrostatic moment and a force from an electromagnetic field, attributed to the presence of a located point charge on this axis. The regulating equations of motion that are pertaining to the equations Euler–Poisson are solved through the utilization of Poincaré’s small parameter method along with its adaptations when the scenario of irrational frequencies is considered. The three angles of Euler are derived and graphed to ascertain the body’s position at any point throughout the motion. The temporal evolutions of the achieved outcomes are drawn to showcase the significant impact of the selected parameters on the motion. The phase plane diagrams have been generated to illustrate the stability of the body during the motion. The novelty of studying the rotatory motion of a charged RB under these specific conditions lies in the intricate interplay of gyrostatic effects, magnetic interactions, and nonlinear dynamics. This research can push the boundaries of theoretical mechanics and provide valuable insights and tools for both theoretical advancements and practical applications. Moreover, the achieved results from this analysis can be utilized to improve the dynamic performance of diverse engineering applications, particularly those dependent on gyroscopic theory. This includes enhancing the functionality of satellites, compasses, submarines, and automatic pilots used in aircraft. Essentially, the findings have practical implications for optimizing the performance and stability of these systems.

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Modeling the optimal deceleration for asymmetric rigid body motion under the influence of a gyrostatic moments and viscous friction

Amer,

Abady,

Abdo

et al. 2024

Journal of Low Frequency Noise, Vibration and Active Control

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This study focuses on determining the required minimum-time (MT) for the spatial motion of a free rigid body (RB) experiencing gyrostatic moments (GMs) and viscous friction. The study assumes that the body’s center of mass coincides with the original point of two Cartesian systems of coordinates. An optimal control law for slow motion is established, and the corresponding time and phase pathways are analyzed. The innovative results are presented for two new cases through various graphs highlighting the positive effects of the GMs. A comparison is achieved between the obtained results and previous outcomes that did not consider gyrostatic moments, showing remarkable consistency with slight deviations that are discussed. The practical applications of this study, which limits itself to using gyroscopic theory to maintain the stability and balance of vehicles in which gyroscopes are used, as well as figuring out the trajectory of aircraft and marine vehicles, are what make it noteworthy.

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Analyzing the spatial motion of a rigid body subjected to constant body-fixed torques and gyrostatic moment

Cited by 5 publications

References 26 publications

Analyzing the dynamics of a charged rotating rigid body under constant torques

Analyzing the dynamics of a charged rotating rigid body under constant torques

The asymptotic solutions for the motion of a charged symmetric gyrostat in the irrational frequency case

Modeling the optimal deceleration for asymmetric rigid body motion under the influence of a gyrostatic moments and viscous friction

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