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Mathematical Control and Related Fields (MCRF)
 

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

Pages: 287 - 302, Volume 3, Issue 3, September 2013      doi:10.3934/mcrf.2013.3.287

 
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Bernard Bonnard - Institut de mathématiques de Bourgogne, 9 avenue Savary, 21078 Dijon, France (email)
Olivier Cots - INRIA Sophia Antipolis Méditerranée, B.P. 93, route des Lucioles, 06902 Sophia Antipolis, France (email)
Nataliya Shcherbakova - INRIA Sophia Antipolis Méditerranée, B.P. 93, route des Lucioles, 06902 Sophia Antipolis, France (email)

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.

Received: December 2012;      Revised: March 2013;      Available Online: September 2013.

 References