Republication of: On the motion of spinning particles in general relativity by Jean-Marie Souriau

This paper was a pioneering contribution to a symplectic description of the dynamics of spinning particles in general relativity which remained somewhat unnoticed. In particular, it introduced the pre-symplectic 2-form \(\sigma \) $\sigma$ describing the dynamics of spinning particles coupled to an Einsteinian curved background. The method throws light on approaches to spinning black holes and neutron stars.