Studying the vibrational motion of a rotating symmetrically charged solid body subjected to external forces and moments

Abstract

This paper studies the rotatory vibrating motion of a dynamically symmetric charged solid body (SB) connected with a spring around a fixed point as a novel model. The body is assumed to be influenced by a Newtonian force field (NFF) besides extrinsic moments like perturbing, restoring, and gyrostatic moment (GM). These moments are guided along the body’s principal axes of inertia. The body is assumed to have a high starting angular velocity in the direction of the dynamic symmetry axis, and the perturbing moments (PM) are thought to be less than the restoring moment. These assumptions provide us with a tiny parameter, to use the averaging technique (AT), and to acquire the averaging system of the regulating one. Several applications are introduced to achieve the solutions of this system separately. These solutions are graphed to reveal the positive influences of the body’s numerical values on the behavior of the body, taking into account the various impacts of the applied moments, the electromagnetic field, and the Newtonian one for all examined applications. The obtained results are considered a generalization of those which were obtained in related previous works. For the projections of the body angular velocity, the proportion of differences as a function of the investigated parameters varies between 17% and 35%, whereas the other parameters are varied between 0.0011% and 0.37%, respectively. Therefore, these outcomes are considered to be significant due to their applications in life specially that based on the theory of vibrating systems in physics and engineering fields.