article · The European Physical Journal Plus
This research investigates the rotational motion and stability of a charged rigid body enclosing a spherical cavity filled with an incompressible viscous liquid. By accounting for a gyrostatic moment, body-fixed constant torques, and resistant torques arising from the liquid shape, the governing equations of motion are formulated via Euler's equations under low Reynolds number conditions. An averaging method alongside Taylor's method and asymptotic techniques are applied to solve the dynamic system under specific initial conditions. Numerical simulations and phase plane diagrams illustrate how variations in electric charge, gyrostatic moments, and resisting forces alter the body's rotational trajectory and motion stability. The resulting mathematical model generalises earlier findings that omitted either the body's charge or the gyrostatic moment, providing a comprehensive framework for analysing fluid-structure interactions during rotational movement.
Understanding how internal liquids affect rotating structures is vital when designing vehicles that carry fluid payloads. Liquid sloshing and internal friction can destabilise a moving craft, creating unexpected oscillations. By providing a generalised mathematical model of motion and stability under combined electrical, gyrostatic, and fluid forces, this work aids the fundamental comprehension of complex dynamic interactions in fluid-filled systems.
The mathematical findings could assist aerospace engineers and transport designers working on control systems for spaceships and rail wagons carrying liquid fuel. However, the study remains at an early theoretical stage, relying on numerical simulations, asymptotic formulations, and phase plane analyses rather than physical prototyping or operational testing. Substantial empirical testing in hardware or scale models would be necessary before these formulations can directly inform vehicle design or control algorithms.
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Abstract The 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.
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DOI: 10.1140/epjp/s13360-023-04581-2
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