  We add to Galilean symmetries the transformations describing constant
accelerations. The corresponding extended Galilean algebra allows, in any
dimension $D=d+1$, the introduction of one central charge $c$ while in $D=2+1$
we can have three such charges: c, \theta and \theta'.
  We present nonrelativistic classical mechanics models, with higher order time
derivatives and show that they give dynamical realizations of our algebras. The
presence of central charge $c$ requires the acceleration square Lagrangian
term. We show that the general Lagrangian with three central charges can be
reinterpreted as describing an exotic planar particle coupled to a dynamical
electric and a constant magnetic field.
