The asymptotic solutions of the governing system of a charged symmetric body under the influence of external torques

Abstract

This paper investigates the motion of a dynamically symmetric rigid body about one of its fixed points in which it is incurred to Newtonian force field, electromagnetic field and external torques. These torques acted in the direction of the principal axes of the body and are represented by perturbing and gyrostatic torques. The body rotates initially about the symmetry dynamic axis with high angular velocity. Therefore, a small parameter can be introduced. The averaging method is applied to convert the governing system of motion into another convenient averaging one in terms of a small parameter. The asymptotic analytical solutions of the latter system are obtained for some distinct applications depending upon the perturbing torques and the restoring one. The good effect of the body parameters on the motion is clarified in the graphical representations of the obtained solutions of the considered applications. The significance of this work is due to its great implementation of practical life like submarines, devices that maintain the stability and measure the orientations of airplanes and for several physics and engineering applications.

Keywords

• Rigid body
• Euler's dynamic equations
• Newtonian field
• Perturbation methods
• Gyrostatic moment
• Perturbing moment