Lagrangian theory of the motion of spinning particles in torsion gravitational theories

The (second-order differential) equations of motion of spinning test particles (tops) are derived from a variational principle in a given gravitational background defined by a Riemannian metric and a torsion tensor. The mass and (magnitude of) the spin of the top are conserved. There exists a Regge trajectory linking the mass and the spin of the top. Constants of the motion associated with Killing vectors of the metric along which the Lie derivative of the torsion tensor vanish are found.