A new algorithm for the Lie transformation View Full Text


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Article Info

DATE

1970-03

AUTHORS

William A. Mersman

ABSTRACT

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. More... »

PAGES

81-89

References to SciGraph publications

  • 1969-03. Canonical transformations depending on a small parameter in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1970. A Unified Treatment of Lunar Theory and Artificial Satellite Theory in PERIODIC ORBITS, STABILITY AND RESONANCES
  • 1969-06. Expansion formulae in canonical transformations depending on a small parameter in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf01230434

    DOI

    http://dx.doi.org/10.1007/bf01230434

    DIMENSIONS

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