# Generating function in action-angle method and Hamilton-Jacobi theory

I think that in action angle method, generating function which generates such a canonical transformation does not explicitly depend on time, so new and old hamiltonians are equal. But in H-J method, generating functions are explicitly dependent upon time. Can some one please clarify this?

1. Hamilton's principal function $$S(q,\alpha,t)$$ and
2. Hamilton's characteristic function $$W(q,\alpha)$$ for time-independent systems.