New action principle for classical particle trajectories in spaces with torsion

To comply with recent developments of path integrals in spaces with curvature and torsion, we find the correct variational principle for classical trajectories of spinless point-particles in such spaces. Although the action depends only on the length, the trajectories are autoparallels (straightest lines) rather than geodesics (shortest lines), due to the effects of a torsion force arising from a geometric peculiarity of the variational procedure.