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This article is cited in 15 scientific papers (total in 15 papers)
On the orbital stability of pendulum-like motions of a rigid body in the Bobylev–Steklov case
B. S. Bardin Department of Theoretical Mechanics, Moscow Aviation Institute,
Volokolamskoe Shosse 4, Moscow 125993, Russia
Abstract:
We deal with the problem of orbital stability of pendulum-like periodic motions of a heavy rigid body with a fixed point. We suppose that the geometry of the mass of the body corresponds to the Bobylev–Steklov case. Unperturbed motion represents oscillations or rotations of the body around a principal axis, occupying a fixed horizontal position. The problem of the orbital stability is considered on the basis of a nonlinear analysis.
In the case of oscillations with small amplitudes as well as in the case of rotations with high angular velocities we study the problem analytically. In the general case we reduce the problem to the stability study of a fixed point of the symplectic map generated by equations of perturbed motion. We calculate coefficients of the symplectic map numerically. By analyzing the abovementioned coefficients we establish the orbital stability or instability of the unperturbed motion. The results of the study are represented in the form of a stability diagram.
Keywords:
Hamiltonian system, periodic orbits, normal form, resonance, action-angel variables, KAM theory.
Received: 28.12.2009 Accepted: 23.02.2010
Citation:
B. S. Bardin, “On the orbital stability of pendulum-like motions of a rigid body in the Bobylev–Steklov case”, Regul. Chaotic Dyn., 15:6 (2010), 704–716
Linking options:
https://www.mathnet.ru/eng/rcd529 https://www.mathnet.ru/eng/rcd/v15/i6/p704
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