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.
This work was supported by the grant of the Russian Scientific Foundation (project No. 19-11-00116) at
the Moscow Aviation Institute (National Research University).
Citation:
B. S. Bardin, E. A. Chekina, “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., 17:4 (2021), 453–464
\Bibitem{BarChe21}
\by B. S. Bardin, E. A. Chekina
\paper On the Orbital Stability of Pendulum-like Oscillations
of a Heavy Rigid Body with a Fixed Point in the
Bobylev – Steklov Case
\jour Rus. J. Nonlin. Dyn.
\yr 2021
\vol 17
\issue 4
\pages 453--464
\mathnet{http://mi.mathnet.ru/nd770}
\crossref{https://doi.org/10.20537/nd210407}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85123557535}
Linking options:
https://www.mathnet.ru/eng/nd770
https://www.mathnet.ru/eng/nd/v17/i4/p453
This publication is cited in the following 2 articles:
José Laudelino de Menezes Neto, Hildeberto Eulálio Cabral, “Nonlinear stability of a pendulum with variable length in elliptic orbit”, São Paulo J. Math. Sci., 19:1 (2025)
B. S. Bardin, A. A. Savin, “On the orbital stability of pendulum periodic motions of a rigid body in the Hess case”, Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, 515:1 (2024), 66
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