A Lax pair for Kowalevski's top
type: Item
instance of: scholarly article
title: A Lax pair for Kowalevski's top
zbMATH Open document ID: 0627.58026
DOI: 10.1016/0167-2789(87)90053-4
author: Luc Haine
author: Emil Horozov
published in: Physica D
publication date: 1987-01-01T00:00:00Z
review text: We show that on each level surface of the invariants, the equations of the Kowalevski top are equivalent to a Neumann system describing the motion of a mass point on the sphere \(S^ 2:| p| =1\) under the influence of a force -Qp. This allows us to write a global Lax pair for the Kowalevski system and to show that Kowalevski's original reduction of the integration of the equations of motion to Jacobi's inversion theorem is identical to the introduction of ``elliptical spherical coordinates'' for integrating C. Neumann's system.
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 14H99
zbMATH DE Number: 4020052
zbMATH Keywords: Kowalevski top
zbMATH Keywords: global Lax pair
zbMATH Keywords: Neumann's system
MaRDI profile type: Publication
full work available at URL: 0167-2789(87)90053-4
OpenAlex ID: W2019449239
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description: scientific article; zbMATH DE number 4020052