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

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.
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https://hal.archives-ouvertes.fr/hal-00908905
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Submitted on : Monday, November 25, 2013 - 2:47:50 PM
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Bernard Bonnard, Olivier Cots, Nataliya Shcherbakova. The Serret-Andoyer Riemannian metric and Euler-Poinsot rigid body motion. Mathematical Control and Related Fields, AIMS, 2013, 3, pp.287-302. ⟨10.3934/mcrf.2013.3.287⟩. ⟨hal-00908905⟩

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