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

Bonnard, Bernard and Cots, Olivier and Shcherbakova, Nataliya Riemannian metrics on 2D manifolds related to the Euler-Poinsot rigid body problem. (2014) In: 52nd IEEE Conference on Decision and Control (CDC 2013), 10 December 2013 - 13 December 2013 (Firenze, Italy).

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Official URL: http://dx.doi.org/10.1109/CDC.2013.6760144

Abstract

The Euler-Poinsot rigid body problem is a well known model of left-invariant metrics on SO(3). In the present paper we discuss the properties of two related reduced 2D models: the sub-Riemanian metric of a system of three coupled spins and the Riemannian metric associated to the Euler- Poinsot problem via the Serret-Andoyer reduction. We explicitly construct Jacobi fields and explain the structure of conjugate loci in the Riemannian case and give the first numerical results for the spin dynamics case.

Item Type:Conference or Workshop Item (Paper)
Additional Information:Thanks to IEEE editor. The definitive version is available at http://ieeexplore.ieee.org This papers appears in Proceedings of CDC 2013. ISSN: 0191-2216 ISSN: 0191-2216 The original PDF of the article can be found at: http://ieeexplore.ieee.org/document/6760144/ Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
HAL Id:hal-01475271
Audience (conference):International conference proceedings
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - INPT (FRANCE)
French research institutions > Institut National de la Recherche en Informatique et en Automatique - INRIA (FRANCE)
Other partners > Université de Bourgogne - UB (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
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Deposited By: IRIT IRIT
Deposited On:03 Feb 2017 09:57

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