Direct Canonical Transformations

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Abstract
Some of the perturbation methods in classical Hamiltonian mechanics lead to near-identity transformations of the variables, with the new variables explicitly given as functions of the old ones. Two methods are used for identifying and characterizing the subclass of all such transformations which are also canonical: one approach is related to the conventional method of generating canonical transformations, while the other one uses the properties of Poisson brackets and is related to an operator method of Lie. Either of the methods may be used to derive certain steps in a perturbation method devised by Lacina, inadvertently omitted by that author.

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