New integrable problem of classical mechanics
type: Item
instance of: scholarly article
title: New integrable problem of classical mechanics
zbMATH Open document ID: 0576.70004
DOI: 10.1007/BF01209304
published in: Communications in Mathematical Physics
publication date: 1984-01-01T00:00:00Z
review text: The main result is that the rotation of an arbitrary rigid body with a fixed point in a Newtonian field given by an arbitrary quadratic potential is completely integrable in the sense of Liouville's integrability theorem. The dynamical equations are integrated explicitely in terms of the Riemann \(\theta\)-functions of four variables, restricted to a three-dimensional manifold (a Prym variety). As a consequence of this the rotation of a rigid body fixed at its center of mass under the action of a Newtonian field of a remote gravitating object is completely integrable in the second order approximation.
Mathematics Subject Classification ID: 70E15
zbMATH DE Number: 3922030
zbMATH Keywords: Riemann theta-function
zbMATH Keywords: integrable problem
zbMATH Keywords: Newtonian field
zbMATH Keywords: quadratic potential
zbMATH Keywords: Liouville's integrability theorem
zbMATH Keywords: Prym variety
author: Oleg I. Bogoyavlenskij
reviewed by: Klaus Horneffer
MaRDI profile type: Publication
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Wikidata QID: Q125898472
description: scientific article; zbMATH DE number 3922030