This article is cited in 2 papers

Nonlinear physics and mechanics

On the Orbital Stability of Pendulum-like Oscillations of a Heavy Rigid Body with a Fixed Point in the Bobylev – Steklov Case

B. S. Bardin^abc, E. A. Chekina<sup>a

a</sup> Moscow Aviation Institute (National Research University), Volokolamskoe sh. 4, Moscow, 125993 Russia
^b Mechanical Engineering Research Institute of the Russian Academy of Sciences, M. Kharitonyevskiy per. 4, Moscow, 101990 Russia
^c Moscow Automobile and Road Construction State Technical University (MADI), Leningradsky pr. 64, Moscow, 125319 Russia

Abstract: 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.

MSC: 34D20, 37J40, 70K30, 70K45, 37N05

Received: 07.12.2021
Accepted: 15.12.2021

Language: English

DOI: 10.20537/nd210407

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