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We consider a closed three-dimensional contact sub-Riemannian manifold. Theobjective of this note is to provide a precise description of thesub-Riemannian geodesics with large initial momenta: we prove that they "spiralaround the Reeb orbits", not only in the phase space but also in theconfiguration space. Our analysis is based on a normal form along any Reeborbit due to Melrose.

Spiraling of sub-Riemannian geodesics around the Reeb flow in the 3D contact case