The Serret-Andoyer Riemannian metric and Euler-Poinsot rigid body motion

Bernard Bonnard; Olivier Cots; Nataliya Shcherbakova

doi:10.3934/mcrf.2013.3.287

Article Contents

2013, Volume 3, Issue 3: 287-302. Doi: 10.3934/mcrf.2013.3.287

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The Serret-Andoyer Riemannian metric and Euler-Poinsot rigid body motion

1.
Institut de mathématiques de Bourgogne, 9 avenue Savary, 21078 Dijon
2.
INRIA Sophia Antipolis Méditerranée, B.P. 93, route des Lucioles, 06902 Sophia Antipolis

Received: November 30, 2012

Revised: February 28, 2013

Published: August 2013

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Abstract

The Euler-Poinsot rigid body motion is a standard mechanical system and is the 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 work [4] on surfaces of revolution.

Keywords:

Euler-Poinsot rigid body motion,
conjugate locus on surfaces of revolution.

Mathematics Subject Classification: 49K15, 53C20, 70Q05.

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