Lagrangian Hamiltonian

1. Jul 4, 2007

Klaus_Hoffmann

for a Lagrangian of the form $$L(q,\dot q , t)$$ we can always construct (except perhaps some counterexamples) the Hamiltonian, but what happens with lagrangians of the form

$$L ( U , U_{i}, i )$$ where i=x,y,z (3-D lagrangian) then i know that the momenta are defined by.

$$\Pi _{U}= \frac{\partial L}{ \partial \dot U}$$

where dot is differentiantion respect to time, but what happens with the terms U_x U_y and U_z can be defined in terms of certain conjugate momenta