THE MOTION OF CROSS-SHAPED BODIES AROUND A FIXED-POINT IN A CENTRAL NEWTONIAN FORCE-FIELD

An octahedral body with identical masses placed at opposite vertices m oves around a fixed point in a central held of Newtonian attraction. T he body is suspended at its centre of mass, which coincides with its g eometrical centre, and the dimensions of the body and the masses conce ntrated at the vertices are such that all principal central moments of inertia are equal. The problem of whether steady motions of such a bo dy exist is considered, and the stability and bifurcations of certain classes of solutions are investigated. The results are compared with s imilar results for steady motions of a rigid body whose mass distribut ion admits of the symmetry group of a regular octahedron [1]. (C) 1996 Elsevier Science Ltd.