Modeling and analysis of the nonlinear rotatory motion of an electromagnetic gyrostat

Abstract

This paper investigates the three-dimensional rotary motion of a charged rigid body (gyrostat) about a fixed point close to the case of Lagrange. We mainly consider the motion under the influence of some forces and moments, on the gyrostat, such as a Newtonian force field in addition to perturbing, gyrostatic, and restoring moments. The body is assumed to have an initially extremely large angular velocity along the direction of the axis of dynamical symmetry and the perturbing moments are smaller than the moment of restoring. Next, the averaging method is used to obtain the averaging system of motion in view of these conditions. The angles of precession and nutation are evaluated asymptotically as new aspects of the orientation of the body at any instant. The graphical performance of these angles is plotted to display the good influence of the applied moments on the motion. In addition, the Runge-Kutta method of fourth-order is applied to get the numerical results of the governing system of motion and these results are represented in other plots. The significance of the current work is due to its various implementations in the theory of gyroscopic motion especially in the design of aircraft, spaceships, and submarines because they are mainly responsible for directing these vehicles.

Keywords

• Gyrostatic motion
• Euler-Poisson equations
• Newtonian field
• Averaging method