  A comparison between the two possible variational principles for the study of
a free falling spinless particle in a space-time with torsion is noted. It is
well known that the autoparallel trajectories can be obtained from a
variational principle based on a non-holonomic mapping, starting with the
standard world-line action. In a contrast, we explore a world-line action with
a modified metric, thinking about the old idea of contorsion (torsion)
potentials. A fixed-ends variational principle can reproduce autoparallel
trajectories without restrictions on space-time torsion. As an illustration we
have considered a perturbative Weitzenb$\ddot{o}$ck space-time. The
non-perturbative problem is stablished at the end.
