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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?

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It seems OP is essentially talking about the difference between

  1. Hamilton's principal function $S(q,\alpha,t)$ and

  2. Hamilton's characteristic function $W(q,\alpha)$ for time-independent systems.

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  • $\begingroup$ so Hamilton's characteristic function generates new hamiltonian in action angle theory, am I right ?? $\endgroup$ – robin raj Nov 8 '18 at 16:40

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