  We consider a relativistic extended object described by a reparametrization
invariant local action that depends on the extrinsic curvature of the
worldvolume swept out by the object as it evolves. We provide a Hamiltonian
formulation of the dynamics of such higher derivative models which is motivated
by the ADM formulation of general relativity. The canonical momenta are
identified by looking at boundary behavior under small deformations of the
action; the relationship between the momentum conjugate to the embedding
functions and the conserved momentum density is established. The canonical
Hamiltonian is constructed explicitly; the constraints on the phase space, both
primary and secondary, are identified and the role they play in the theory
described. The multipliers implementing the primary constraints are identified
in terms of the ADM lapse and shift variables and Hamilton's equations shown to
be consistent with the Euler-Lagrange equations.
