The Hamiltonian dynamics of the two gyrostats problem
type: Item
instance of: scholarly article
title: The Hamiltonian dynamics of the two gyrostats problem
zbMATH Open document ID: 0965.70013
DOI: 10.1023/A:1008375820146
author: Félix Mondéjar
author: A. Vigueras
published in: Celestial Mechanics and Dynamical Astronomy
publication date: 1999-01-01T00:00:00Z
review text: The authors discuss the problem of two gyrostats in a central force field, considering the mutual interaction between orbital and rotational motion. It is proved that the Newton-Euler equations are Hamiltonian with respect to a certain non-canonical structure. The authors show that the number of degrees of freedom can be reduced, and give an explicit form of the corresponding non-canonical Poisson bracket. In a special case when one of the gyrostats has null gyrostatic momentum, all equilibria are unstable in the zeroth-order approximation.
Mathematics Subject Classification ID: 70E05
Mathematics Subject Classification ID: 70H05
Mathematics Subject Classification ID: 70E50
zbMATH DE Number: 1442272
zbMATH Keywords: unstable equilibria
zbMATH Keywords: non-canonical Hamiltonian structure
zbMATH Keywords: two gyrostats
zbMATH Keywords: central force field
zbMATH Keywords: Newton-Euler equations
zbMATH Keywords: non-canonical Poisson bracket
zbMATH Keywords: null gyrostatic momentum
zbMATH Keywords: zeroth-order approximation
reviewed by: Yan-Zhu Liu
MaRDI profile type: Publication
full work available at URL: a:1008375820146
OpenAlex ID: W4244913219
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description: scientific article; zbMATH DE number 1442272