The Goryachev-Chaplygin top and the Toda lattice
type: Item
instance of: scholarly article
title: The Goryachev-Chaplygin top and the Toda lattice
zbMATH Open document ID: 0638.58010
DOI: 10.1007/BF01207371
author: C. Bechlivanidis
author: Pierre van Moerbeke
published in: Communications in Mathematical Physics
publication date: 1987-01-01T00:00:00Z
review text: The Goryachev-Chaplygin top is known to be a completely algebraically integrable system as a linear flow on a hyperelliptic Jacobian. In this paper it is proved that the invariant surfaces of the Goryachev-Chaplygin top are double covers of the Jacobian above ramified along the two translates of the theta divisor, touching in one point. The equations of motion for the Goryachev-Chaplygin top are shown to be an instance of a system of differential equations in 7 unknowns having 5 quadratic constants of motion which is related intimately with the system of equations for the 3-body periodic Toda lattice.
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 37N99
zbMATH DE Number: 4040875
zbMATH Keywords: Goryachev-Chaplygin top
zbMATH Keywords: integrable system
zbMATH Keywords: linear flow on a hyperelliptic Jacobian
zbMATH Keywords: 3-body periodic Toda lattice
reviewed by: E. D. Belokolos
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01207371
OpenAlex ID: W2000235662
description: scientific article; zbMATH DE number 4040875