Preprints, Working Papers, ... Year : 2013

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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Dates and versions

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

Identifiers

  • HAL Id : hal-00918587 , version 1

Cite

Bernard Bonnard, Olivier Cots, Nataliya Shcherbakova. RIEMANNIAN METRICS ON 2D-MANIFOLDS RELATED TO THE EULER-POINSOT RIGID BODY MOTION.. 2013. ⟨hal-00918587v1⟩
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