Lie Transforms and the Hamiltonization of Non-Hamiltonian Systems

Details Lie Transforms and the Hamiltonization of Non-Hamiltonian Systems Lie Transforms and the Hamiltonization of Non-Hamiltonian Systems

Dec 1971

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1971cemec...4..397k&link_type=abstract

Celestial Mechanics, Volume 4, Issue 3-4, pp. 397-405

Physics

8

Scientific paper

To develop the perturbation solution of the non-Hamiltonian system of differential equationsy=g(y, t; ɛ), it is sufficient to obtain the perturbation solution of a Hamiltonian system represented by the HamiltonianK=Y·g(y, t; ɛ) which is linear in the adjoint vectorY. This Hamiltonization allows the direct use of the perturbation methods already established for Hamiltonian systems. To demonstrate this fact, a Hamiltonian algorithm developed by this author and based on the Lie-Deprit transform is applied to the Hamiltonized system and is shown to be equivalent to the application of the non-Hamiltonian form of this same algorithm to the original non-Hamiltonian system.

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