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

International audienceThe 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