Analyzing the Motion of a Charged Rigid Body under the Influence of a Gyrostatic Torque

Abstract

This research investigates the rotational dynamics of a charged axisymmetric spinning rigid body influenced by gyrostatic torque. The study also accounts for the effects of transverse and constant body-fixed torques and an electromagnetic force field. Euler's equations of motion are employed to formulate the governing equations for the system. Given the absence of torque along the spin axis and the nearly symmetric structure of the rigid body, the spin rate remains almost constant. By assuming small angular deviations of the spin axis from a fixed spatial direction, approximate analytical solutions in closed form are derived for the attitude, translational, and rotational motions. These solutions, expressed in a compact complex form, provide an effective tool for analyzing the maneuvers of rigid bodies spinning. The study derives analytical solutions for several variables, including angular velocities, Euler angles, transverse and axial displacements, and velocities. Graphical simulations of the solutions demonstrate their accuracy, while additional graphs illustrate the positive effects of varying body parameters on the motion. This work is significant in diverse scientific and engineering fields, offering insights that enhance the design of mechanical systems, explain celestial dynamics, and improve spacecraft performance.