The separatrix of an unstable position of equilibrium of a Hess-Appelrot gyroscope
type: Item
instance of: scholarly article
title: The separatrix of an unstable position of equilibrium of a Hess-Appelrot gyroscope
zbMATH Open document ID: 0809.70004
DOI: 10.1016/0021-8928(92)90009-W
author: S. A. Dovbysh
published in: Journal of Applied Mathematics and Mechanics
publication date: 1994-03-07T00:00:00Z
review text: A heavy rigid body rotating about a fixed point, whose inertial tensor and the centre of mass satisfy the Hess-Appelrot conditions, is considered. The gyroscope has an unstable position of equilibrium at which the radius-vector from the point of support to the centre of mass is directed vertically upwards at the zeroth value of area integral constant. The motion close to the paired separatrices is considered, and a set of long-period solutions are obtained. The splitting of the separatrices of perturbed unstable permanent rotation is studied using first-order perturbation theory. The same problem for a perturbed Lagrange gyroscope is discussed as a special case of Hess-Appelrote gyroscope.
Mathematics Subject Classification ID: 70E05
Mathematics Subject Classification ID: 70K20
zbMATH DE Number: 500932
zbMATH Keywords: paired separatrices
zbMATH Keywords: long-period solutions
zbMATH Keywords: splitting
zbMATH Keywords: first-order perturbation theory
zbMATH Keywords: perturbed Lagrange gyroscope
reviewed by: Yan-Zhu Liu
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 500932