Invariant sets in the Goryachev–Chaplygin problem: existence, stability and branching

The existence, stability and branching of invariant sets in the problem of the motion of a heavy rigid body with a fixed point, which satisfies the Goryachev–Chaplygin conditions, are discussed. Both trivial invariant sets, in which the pendulum-like motions of a Goryachev–Chaplygin spinning top lie, as well as non-trivial invariant sets, in which the motion of the top is described by elliptic functions of time, are investigated.