THE STEADY MOTIONS OF A SYSTEM OF 2 ELASTICALLY COUPLED BODIES

The problem of the existence, branching and stability of the steady mo tions of a system of two elastically coupled bodies in a central gravi tational field is considered. Each body is simulated by a weightless r od with point masses at opposite ends. It is assumed that the rods are elastically 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 v ector 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 stabilit y of all steady motions is fully investigated and an atlas of bifurcat ion diagrams presented. (C) 1998 Elsevier Science Ltd. All rights rese rved.