Gravitationally Stabilized Rigid Bodies and Gyrostats

Abstract

The classical libration problem of Lagrange is one forerunner of the analogous problem for the gyrostat. Another is the problem of an orbiting symmetric spinning body ated upon by gravitational torques. The equilibrium orientation of such a body with its spin axis normal to the plane of the (circular) orbit is implicit in several works on spin stabilization; but the first to treat its stability explicitly was Thomson [1]. (His stability phase diagram was incomplete, and was extended by Kane, Marsh and Wilson [2] shortly thereafter.) Likins [3] was the first to demonstrate that a spinning body can have other equilibrium orientations of the spin axis besides the one normal to the orbit plane: specifically, the spin axis can remain in the plane normal to the orbital path but inclined to the orbit normal, or in the plane normal to the local geocentric vertical and again inclined to the orbit normal. These equilibria have precise counterparts in the case of the orbiting gyrostat.