Aa. Burov, THE MOTION OF CROSS-SHAPED BODIES AROUND A FIXED-POINT IN A CENTRAL NEWTONIAN FORCE-FIELD, Journal of applied mathematics and mechanics, 60(1), 1996, pp. 25-30
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.