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

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


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