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
Document type :
Journal articles
Complete list of metadatas

Cited literature [24 references]  Display  Hide  Download
https://hal.inria.fr/hal-00918587
Contributor : Olivier Cots <>
Submitted on : Tuesday, January 14, 2014 - 4:24:47 PM
Last modification on : Sunday, June 30, 2019 - 10:40:05 AM
Long-term archiving on : Tuesday, April 15, 2014 - 4:26:50 PM

File

euler_andoyer_cocv_final_.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00918587, version 2

Collections

INRIA | UNIV-BOURGOGNE | IMB_UMR5584 | INSMI | DIEUDONNE | TDS-MACS | UNIV-TLSE3

Citation

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⟩

Export

BibTeX TEI DC DCterms EndNote

Share

Metrics

Record views

660

Files downloads

944

Contact


archive-ouverte@inria.fr