Riemannian metrics on 2D-manifolds related to the Euler-Poinsot rigid body motion - Archive ouverte HAL Access content directly
Journal Articles ESAIM: Control, Optimisation and Calculus of Variations Year : 2014

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

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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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Dates and versions

hal-00918587 , version 1 (13-12-2013)
hal-00918587 , version 2 (14-01-2014)

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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, 2014, 20 (3), pp.864-893. ⟨10.1051/cocv/2013087⟩. ⟨hal-00918587v2⟩
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