| Issue |
ESAIM: COCV
Volume 20, Number 3, July-September 2014
|
|
|---|---|---|
| Page(s) | 864 - 893 | |
| DOI | https://doi.org/10.1051/cocv/2013087 | |
| Published online | 10 June 2014 | |
Riemannian metrics on 2D-manifolds related to the Euler−Poinsot rigid body motion∗
1
Institut de Mathématiques de Bourgogne,
9 avenue Savary,
21078
Dijon,
France
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2
INRIA Sophia-Antipolis Méditerranée, 2004, route des Lucioles,
06902
Sophia Antipolis,
France
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3
Université de Toulouse, INPT, UPS, Laboratoire de Génie Chimique,
4 allée Emile
Monso, 31432
Toulouse,
France
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Received: 20 May 2013
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.
Mathematics Subject Classification: 49K15 / 53C20 / 70Q05 / 81Q93
Key words: Euler−poinsot rigid body motion / conjugate locus on surfaces of revolution / Serret−Andoyer metric / spins dynamics
Work supported by ANR Geometric Control Methods (project No. NT09504490).
© EDP Sciences, SMAI, 2014
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