The steady motions of a system of two elastically coupled bodies

The problem of the existence, branching and stability of the steady motions of a system of two elastically coupled bodies in a central gravitational field is considered. Each body is simulated by a weightless rod with point masses at opposite ends. It is assumed that the rods are essentially attached at their mass centres, and the composite body is moving in a plane containing the attracting centre. Both trivial and non-trivial steady motions are studied, on the assumption that none of the principal axes of inertia of the body coincides with the radius vector of the centre of mass or with a tangent to the orbit; it is also assumed that the rods are not orthogonal to one another. The stability of all steady motions is fully investigated and an atlas of bifurcation diagrams presented.