Analysis of the Rotational Motion of a Solid Body in the Presence of External Moments

Abstract

Abstract Purpose In this work, the vibrating motion of a dynamically symmetric solid body with an elastic string, around a fixed point, as a new model, is investigated. Hypotheses The body spins as a result of external moments along the body’s principal axes, such as perturbing, restoring, and gyrostatic moments. It has been supposed that this body has a rapid angular velocity at the beginning of motion in the direction of its symmetry dynamic axis. Methods The averaging approach is employed to transform the governing system of motion into another appropriate averaging one to gain the asymptotic solutions of this system. Conclusion These solutions are graphed and discussed in different plots depending on the numerical values of the body’s physical properties. The positive effects of the gyrostatic moment vector on the motion are examined in some cases. Furthermore, the obtained results generalize the previously related studies. Applications The importance of the investigated dynamical system is due to its applications in a variety of domains, including physics and engineering.