Abstract
The Euler-Poinsot rigid body motion is a standard mechanical systemand is the model for left-invariant Riemannian metrics on $SO(3)$.In this article, using the Serret-Andoyer variables we parameterizethe solutions and compute the Jacobi fields in relation with the conjugatelocus evaluation. Moreover the metric can be restricted to a 2D surfaceand the conjugate points of this metric are evaluated using recentwork [4] on surfaces of revolution.
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