A New Algorithm for the Lie Transformation

Details A New Algorithm for the Lie Transformation A New Algorithm for the Lie Transformation

Mar 1970

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1970cemec...3...81m&link_type=abstract

Celestial Mechanics, Volume 3, Issue 1, pp.81-89

Physics

29

Scientific paper

Following Hori, the Lie transformation is presented in a form that is independent of any extraneous parameters. The transformation is canonical, and its inverse is obtained by changing the sign of the generating function. The introduction of a small parameter into the generating function and the Hamiltonian then yields a recursive, triangular algorithm. The case of a Hamiltonian containing the time explicitly is included by adjoining an additional pair of conjugate variables. The necessary and sufficient condition that this transformation be identical to Deprit's transformation is given as a recursive relation between successive terms in the generating functions. Explicit formulas are obtained through the sixth order.

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