  We study a recently proposed generalization of the relativistic particle by
Kosteleck\'y, that includes explicit Lorentz violation. We present an
alternative action for this system and we show that this action can be
interpreted as a particle in curved space with a metric that depends on the
Lagrange multipliers. Furthermore, the following results are established for
this model: (i) there exists a limit where this system has more local
symmetries that the usual relativistic particle; (ii) in this limit if we
restore the Lorentz symmetry we obtain a direct relationship with the two time
physics; (iii) also we show that if we intent to restore the Poincar\'e
symmetry we obtain the action of the relativistic bosonic string.
