Hamiltonian Mechanics

bon

1. The problem statement, all variables and given/known data

Basically, I'm given a Hamiltonian H = H(p,q) and asked to find a new Hamiltonian K = K(Q,P,t) using the generating functions method

H = 1/2 (p^2 + q^2)

Generating function f(q,P,t) = qp sec ( t ) - 1/2 (q^2 + P^2) tan ( t )


So, I have no problem finding the new K, i just find K = 0.

The question then asks for a physical interpretation of the result.


2. Relevant equations



3. The attempt at a solution

I'm stuck on the physical interpretation. What does it mean if you transform to new coordinates and your new hamiltonian is zero?

Thanks!