Motion of a Rigid Body in a Newtonian Field of Force Exerted by Three Attracting Centers

Abstract

In this paper, a nonsymmetric rigid body rotating around a fixed point under the action of a central Newtonian field of force exerted by three centers of attraction is considered. The angular momentum principle is applied to deduce the equations of motion of this body. These equations represent a simple autonomous system of twelve nonlinear ordinary differential equations, which describe the motion of the body. The first integrals for such a system are obtained. Euler, Lagrange, and the kinetic symmetry cases are obtained as special cases from this problem. The numerical solution for this system is obtained by using the fourth-order Runge-Kutta method. The aim is to find the influence of the characteristic parameters of the body on the motion. Two cases of study are given. The first occurs when the three attracting centers lie on the fixed axes