On the stability of the permanent rotations of an asymmetric heavy rigid body
type: Item
instance of: scholarly article
title: On the stability of the permanent rotations of an asymmetric heavy rigid body
zbMATH Open document ID: 0572.70003
DOI: 10.1016/0021-8928(83)90056-4
author: D. V. Andreev
published in: Journal of Applied Mathematics and Mechanics
publication date: 1984-01-01T00:00:00Z
review text: The stability of the rotations around the vertical axis of an asymmetric heavy rigid body with a fixed point are investigated on the basis of the Arnold-Moser stability theorems for a Hamiltonian system in the nonresonance case, and based on third- and fourth-order resonances investigated by \textit{A. P. Markeev} [ibid. 32, 738-744 (1968; Zbl 0184.119)]. It is shown that in the non-resonance case the stability of all except, perhaps, a finite number, permanent rotations is determined by the first approximation. Stability and instability conditions for resonance rotations are found.
Mathematics Subject Classification ID: 70E05
zbMATH DE Number: 3913737
zbMATH Keywords: rotations around the vertical axis
zbMATH Keywords: asymmetric heavy rigid body
zbMATH Keywords: Arnold- Moser stability theorems
zbMATH Keywords: nonresonance case
zbMATH Keywords: third- and fourth-order resonances
zbMATH Keywords: instability conditions
MaRDI profile type: Publication
full work available at URL: 0021-8928(83)90056-4
OpenAlex ID: W2019898421
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description: scientific article; zbMATH DE number 3913737