  We consider the Regge-Teitelboim model for a relativistic extended object
embedded in a fixed background Minkowski spacetime, in which the dynamics is
determined by an action proportional to the integral of the scalar curvature of
the worldvolume spanned by the object in its evolution. In appearance, this
action resembles the Einstein-Hilbert action for vacuum General Relativity: the
equations of motion for both are second order; the difference is that here the
dynamical variables are not the metric, but the embedding functions of the
worldvolume. We provide a novel Hamiltonian formulation for this model. The
Lagrangian, like that of General Relativity, is linear in the acceleration of
the extended object. As such, the model is not a genuine higher derivative
theory, a fact reflected in the order of the equations of motion. Nevertheless,
as we will show, it is possible as well as useful to treat it as a `fake'
higher derivative system, enlarging the phase space appropriately. The
corresponding Hamiltonian on this phase space is constructed: it is a
polynomial. The complete set of constraints on the phase space is identified.
The fact that the equations of motion are of second order in derivatives of the
field variables manifests itself in the Hamiltonian formulation through the
appearance of additional constraints, both primary and secondary. These new
constraints are second class. In this formulation, the Lagrange multipliers
implementing the primary constraints get identified as accelerations. This is a
generic feature of any Lagrangian linear in the acceleration possessing
reparametrization invariance.
