On the orbital stability of pendulum periodic motions of a rigid body in the Hess case

The problem of orbital stability of pendulum periodic motions of a heavy rigid body with one fixed point is investigated. Based on the analysis of the liberalized system of equations of perturbed motion, the orbital instability of pendulum rotations is proven. In the case of pendulum oscillations, a transcendental situation occurs when the question of stability cannot be solved by terms of an arbitrarily high order in the expansion of the Hamiltonian of the equations of perturbed motion. It is proven that for most values of the parameters, pendulum oscillations are orbitally unstable.