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

Bernard Bonnard 1 Olivier Cots 2, * Jean-Baptiste Pomet 2 Nataliya Shcherbakova 3
* Corresponding author
1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
2 McTAO - Mathematics for Control, Transport and Applications
CRISAM - Inria Sophia Antipolis - Méditerranée
3 LGC - Laboratoire de génie chimique [ancien site de Basso-Cambo]
Abstract : The Euler-Poinsot rigid body motion is a standard mechanical system and is a model for left-invariant Riemannian metric 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 work 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.
Keywords : Euler-Poinsot rigid body motion
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Journal articles
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Submitted on : Tuesday, January 14, 2014 - 4:24:47 PM
Last modification on : Monday, October 14, 2019 - 3:12:02 PM
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  • HAL Id : hal-00918587, version 2

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Bernard Bonnard, Olivier Cots, Jean-Baptiste Pomet, Nataliya Shcherbakova. Riemannian metrics on 2D-manifolds related to the Euler-Poinsot rigid body motion. ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2014. ⟨hal-00918587v2⟩

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