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

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.
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https://hal.inria.fr/hal-00918587
Contributor : Olivier Cots <>
Submitted on : Tuesday, January 14, 2014 - 4:24:47 PM
Last modification on : Monday, October 14, 2019 - 3:12:02 PM
Long-term archiving on : Tuesday, April 15, 2014 - 4:26:50 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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