On the stability of bodies suspended asymmetrically with an inelastic rope

The stability of a body suspended asymmetrically by means of an inelastic rope is investigated. The rope is attached to the body at two points and passed over a frictionless hook or a nail in the vertical plane. The equilibrium points of the system and their stability are described as a function of the rope length, the distance of the attachment points and the position of the center of mass. Depending on the choice of the parameters, one, two or three equilibrium positions exist: their structural change manifests itself in the form of cusp bifurcations of co-dimension two, which is determined in exact analytical form.