The Slow Spinning Motion of a Rigid Body in Newtonian Field and External Torque

Abstract

In this paper, the problem of the slow spinning motion of a rigid body about a point O, being fixed in space, in the presence of the Newtonian force field and external torque is considered. We achieve the slow spin by giving the body slow rotation with a sufficiently small angular velocity component $r_0$ about the moving z-axis. We obtain the periodic solutions in a new domain of the angular velocity vector component $r_0⟶0$ , define a large parameter proportional to $1/r_0$ , and use the technique of the large parameter for solving this problem. Geometric interpretations of motions will be illustrated. Comparison of the results with the previous works is considered. A discussion of obtained solutions and results is presented.