  The canonical structure of theories whose Lagrangian contains higher powers
of time derivatives is often obscured by the nonlinear relationship between the
velocities and momenta. We use the Dirac formalism and define a generalized
Legendre transform to overcome some of the difficulties associated with
inverting the relation between velocities and momenta. We are then able to
define a standard single valued symplectic structure on phase space and a
compatible single valued Hamiltonian. We demonstrate the application of our
formalism in several examples.
