On the Orbital Stability of Periodic Motions of a Heavy Rigid Body in the Bobylev – Steklov Case

The problem of the orbital stability of periodic motions of a heavy rigid body with a fixed point is investigated. The periodic motions are described by a particular solution obtained by D. N. Bobylev and V. A. Steklov and lie on the zero level set of the area integral. The problem of nonlinear orbital stability is studied. It is shown that the domain of possible parameter values is separated into two regions: a region of orbital stability and a region of orbital instability. At the boundary of these regions, the orbital instability of the periodic motions takes place.