A Note on the Rotationally Symmetric SO(4) Euler Rigid Body

2006/11/30 by Gregorio Falqui · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Advanced Differential Geometry Research #Nonlinear Waves and Solitons #math-ph #math.DG #math.MP #msc:14H70 #msc:37K10 #msc:70H20 #nlin.SI

paper · pdf · doi:10.3842/sigma.2007.032

published as SIGMA 3 (2007), 032, 13 pages · This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

arxiv created 2007/02/26 · openalex publication_date 2007/02/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider an SO(4) Euler rigid body with two 'inertia momenta' coinciding. We study it from the point of view of bihamiltonian geometry. We show how to algebraically integrate it by means of the method of separation of variables.

Citations

• Separation of variables on a non-hyperelliptic curve
• Poisson Pencils, Integrability, and Separation of Variables
• Simultaneous separation for the Kowalevski and GoryachevndashChaplygin gyrostats
• Webs, Lenard schemes, and the local geometry of bihamiltonian Toda and Lax structures
• Separation of variables for bi-Hamiltonian systems

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• Canonoid and Poissonoid transformations, symmetries and biHamiltonian structures