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

Bernard Bonnard; Olivier Cots; Jean-Baptiste Pomet; Nataliya Shcherbakova

ESAIM: Control, Optimisation and Calculus of Variations (2014)

  • Volume: 20, Issue: 3, page 864-893
  • ISSN: 1292-8119

Abstract

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The Euler−Poinsot rigid body motion is a standard mechanical system and it is a model for left-invariant Riemannian metrics 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 works 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.

How to cite

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Bonnard, Bernard, et al. "Riemannian metrics on 2D-manifolds related to the Euler−Poinsot rigid body motion." ESAIM: Control, Optimisation and Calculus of Variations 20.3 (2014): 864-893. <http://eudml.org/doc/272921>.

@article{Bonnard2014,
abstract = {The Euler−Poinsot rigid body motion is a standard mechanical system and it is a model for left-invariant Riemannian metrics 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 works 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.},
author = {Bonnard, Bernard, Cots, Olivier, Pomet, Jean-Baptiste, Shcherbakova, Nataliya},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Euler−poinsot rigid body motion; conjugate locus on surfaces of revolution; Serret−Andoyer metric; spins dynamics; Euler-Poinsot rigid body motion; conjugate locus; surfaces of revolution; Serret-Andoyer metric; spin dynamics},
language = {eng},
number = {3},
pages = {864-893},
publisher = {EDP-Sciences},
title = {Riemannian metrics on 2D-manifolds related to the Euler−Poinsot rigid body motion},
url = {http://eudml.org/doc/272921},
volume = {20},
year = {2014},
}

TY - JOUR
AU - Bonnard, Bernard
AU - Cots, Olivier
AU - Pomet, Jean-Baptiste
AU - Shcherbakova, Nataliya
TI - Riemannian metrics on 2D-manifolds related to the Euler−Poinsot rigid body motion
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2014
PB - EDP-Sciences
VL - 20
IS - 3
SP - 864
EP - 893
AB - The Euler−Poinsot rigid body motion is a standard mechanical system and it is a model for left-invariant Riemannian metrics 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 works 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.
LA - eng
KW - Euler−poinsot rigid body motion; conjugate locus on surfaces of revolution; Serret−Andoyer metric; spins dynamics; Euler-Poinsot rigid body motion; conjugate locus; surfaces of revolution; Serret-Andoyer metric; spin dynamics
UR - http://eudml.org/doc/272921
ER -

References

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