The orbital stability of pendulum-like oscillations of a heavy rigid body with a fixed point in
the Bobylev – Steklov case is investigated. In particular, a nonlinear study of the orbital stability
is performed for the so-called case of degeneracy, where it is necessary to take into account terms
of order six in the Hamiltonian expansion in a neighborhood of the unperturbed periodic orbit.
Keywords:
rigid body, rotations, oscillations, orbital stability, Hamiltonian system, local coordinates, normal form
Citation:
Bardin B. S., Chekina E. A., On the Orbital Stability of Pendulum-like Oscillations of a Heavy Rigid Body with a Fixed Point in the Bobylev – Steklov Case, Rus. J. Nonlin. Dyn.,
2021, Vol. 17, no. 4,
pp. 453-464