Homogeneous Stäckel-type systems
type: Item
instance of: scholarly article
title: Homogeneous Stäckel-type systems
zbMATH Open document ID: 0960.37026
DOI: 10.1007/BF02575497
published in: Theoretical and Mathematical Physics
publication date: 2000-06-26T00:00:00Z
review text: Completely integrable systems of Stäckel type are holonomic systems in the phase space \(\mathbb{R}^{2n}\) with Hamiltonian \[ H= \sum_{j=1}^n g_j (q_1,\dots, q_n) (p_j^2+ V_j(q_j)), \] where \(\{p_j, q_j\}\) are canonical variables in \(\mathbb{R}^{2n}\). The author proves that the Stäckel matrix is the derivative of the Abel mapping. The author constructs the Lax representation and studies its properties. Using the representation he constructs curvilinear orthogonal coordinate systems in a flat space and two classes of canonical coordinate transformations related to these systems.
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 70H06
Mathematics Subject Classification ID: 37J15
zbMATH DE Number: 1466068
zbMATH Keywords: holonomic systems
zbMATH Keywords: Hamiltonian
zbMATH Keywords: Stäckel matrix
zbMATH Keywords: curvilinear coordinate system
author: A. V. Tsiganov
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
Wikidata QID: Q124829886
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full work available at URL: https://doi.org/10.1007/bf02575497
OpenAlex ID: W2334640736
description: scientific article; zbMATH DE number 1466068