Lie transforms and the Hamiltonization of non-Hamiltonian systems View Full Text


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Article Info

DATE

1971-12

AUTHORS

Ahmed Aly Kamel

ABSTRACT

To develop the perturbation solution of the non-Hamiltonian system of differential equationsy=g(y, t; ε), 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. More... »

PAGES

397-405

References to SciGraph publications

  • 1969-03. Canonical transformations depending on a small parameter in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1969-06. Expansion formulae in canonical transformations depending on a small parameter in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1970-12. Equivalence of the perturbation theories of Hori and Deprit in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1970-03. Perturbation method in the theory of nonlinear oscillations in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1970-03. A new algorithm for the Lie transformation in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1970-03. On a perturbation theory using Lie transforms in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1971-09. Explicit recursive algorithms for the construction of equivalent canonical transformations in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1970-03. The equivalence of von Zeipel mappings and Lie transforms in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf01231400

    DOI

    http://dx.doi.org/10.1007/bf01231400

    DIMENSIONS

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