Noncanonical Parametrization of Poisson Brackets in Celestial Mechanics

Details Noncanonical Parametrization of Poisson Brackets in Celestial Mechanics Noncanonical Parametrization of Poisson Brackets in Celestial Mechanics

Sep 2001

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2001sosyr..35..415k&link_type=abstract

Solar System Research, v. 35, Issue 5, p. 415-419 (2001).

Physics

Scientific paper

The formulas for the Poisson bracket of a perturbed two-body problem and a perturbed planetary problem are found in different systems of Keplerian elements. As with canonical parametrization, the Poisson bracket is equal to a linear combination of partial brackets, but it contains coefficients depending on semimajor axis, eccentricity, and inclination. A simple relation between the Poisson brackets and matrices of coefficients of Lagrange-type equations determining the variations of osculating elements is derived. The Poisson bracket of D'Alembertian functions is proved to be a D'Alembertian one by itself.

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