A note on the application of a generalized canonical approach to non-linear Hamiltonian systems

In the author's treatment of the ideal resonance problem (1988), a non-canonical transformation was employed to bring the original Hamiltonian to a form amenable to the use of standard action-angle variables. Though the strictly Hamiltonian form of equations of motion was thus compromised, their general form was maintained, allowing transformation of the system to arbitrary order and forestalling the introduction of elliptic functions until a final explicit integration required in this approach. The general theory of such transformations is presented, and some points regarding their application are discussed, leading to the conclusion that the approach is practically limited to systems with a single degree of freedom only.