Evaluating the motion of a charged solid body having a globular cavity

Abstract

The dynamical motion of a charged symmetrical solid body (SB) about its main symmetric axis is addressed in this work. The body is supposed to have a chamber with a globular shape, in which it contains a mobile mass and filled with a viscous liquid. This mass is assumed to be coupled via a double elastic band at a point that is situated along the dynamical symmetry axis and produces viscous friction. The body’s motion is influenced by a gyrostatic moment (GM), whose first two components on the body’s main axes are chosen to be zero. Additionally, the body is subject to the effects of an electromagnetic field, owing to a located point charge on the body’s dynamic symmetry axis. On the indicated motion, the combined impact of the viscous liquid and the mobile mass is investigated. The achieved outcomes show that, in the presence of internal dissipation, the system's motion tends towards a constant rotation around its axis at the point of highest inertia as time approaches infinity. To demonstrate how the body’s parameters affect the motion, the obtained outcomes are graphed. The method of fourth-order Runge-Kutta (4RKM) is employed to generate the governing system's numerical results, which are then displayed in additional diagrams. This work's relevance is concentrated on its considerable potential for usage in the submarine and gyroscope industries. The novelty of this work lies in the intricate interplay of rotational dynamics due to the GM, viscous liquid and electromagnetic effects to achieve new results, besides the gained numerical outcomes. Therefore, these results are considered novel and have significant theoretical and practical relevance. Moreover, it can be used to study the motion of celestial bodies, such as planets or moons, which might have internal cavities filled with fluids or other materials. The charged nature could be relevant for bodies with significant magnetic fields.

Keywords

• Nonlinear dynamics
• Viscous fluid
• Solid body motion
• Gyrostatic moment
• Numerical solution