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Riemannian metrics on 2D-manifolds related to the Euler-Poinsot rigid body motion

Bonnard, Bernard and Cots, Olivier and Pomet, Jean-Baptiste and Shcherbakova, Nataliya Riemannian metrics on 2D-manifolds related to the Euler-Poinsot rigid body motion. (2014) ESAIM : Control, Optimisation and Calculus of Variations, 20 (3). 864-893. ISSN 1292-8119

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Official URL: http://dx.doi.org/10.1051/cocv/2013087

Abstract

The Euler-Poinsot rigid body motion is a standard mechanical system and it is a model for left-invariant Riemannian metrics on SO(3). In this article using the Serret-Andoyer variables we parameterize the solutions and compute the Jacobi fields in relation with the conjugate locus evaluation. Moreover, the metric can be restricted to a 2D-surface, and the conjugate points of this metric are evaluated using recent works on surfaces of revolution. Another related 2D-metric on S2 associated to the dynamics of spin particles with Ising coupling is analysed using both geometric techniques and numerical simulations.

Item Type:Article
Additional Information:Thanks to EDP Sciences editor. The definitive version is available at http://www.esaim-cocv.org/ The original PDF can be found at: http://www.esaim-cocv.org/articles/cocv/pdf/2014/03/cocv130087.pdf
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - INPT (FRANCE)
French research institutions > Institut National de la Recherche en Informatique et en Automatique - INRIA (FRANCE)
Other partners > Université de Bourgogne - UB (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
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Deposited By: IRIT IRIT
Deposited On:02 Feb 2017 09:49

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