On the motion of a flywheel in the presence of attracting center

Abstract

In this work, the rotational motion of a body fixed at one point is investigated when the effectiveness of a Newtonian field is taken into consideration. It is assumed that the center of mass of the body lies on one of the principal planes of inertia. The attained solutions are obtained when the body carrying rotating masses represented by a flywheel or may be multiply-connected cavities containing circulated liquid. Two special cases are evaluated. The Runge-Kutta algorithms from fourth order is applied to achieve the numerical solution of the equations of motion and represented graphically to show the variation of the body’s parameters on the motion. The importance of this work is due to its wide applications in many fields such as in physics, engineering and industrial applications. MSC (2010): 70E05, 70E15, 70E17, 70E20, Keywords: Euler’s equations, Newtonian field, Gyrostatic moment, First integrals