Originally Posted by

**Kiwi_Dave** To answer your questions H is the Hamiltonian.

F is defined by the right hand side. The object of the exercise as I understand it is to demonstrate that the right hand side is equal to the total derivative of some function (which I have called F, if it exists). This would demonstrate that the Lagrangian is divergence invariant under the specified infintesimal transformation.

I don't have an intuitive understanding of what "divergence invariant" means. Perhaps the divergence of F must be zero?