Physics
Scientific paper
Apr 1982
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982m%26p....26..143m&link_type=abstract
Moon and the Planets, vol. 26, Apr. 1982, p. 143-169.
Physics
Canonical Forms, Hamiltonian Functions, Orbital Mechanics, Quadratures, Solar Orbits, Eccentric Orbits, Nonlinear Equations, Perturbation Theory, Planetology
Scientific paper
After solving the first-order nonlinear differential equation, the canonical differential equations resulting from the elimination of short period terms in a second-order planetary theory are reduced to two quadratures. Hori's (1966) method and slow Delaunay canonical variables are used for the cases where powers of eccentricities, and sines of semi-inclinations which are greater than three, are neglected, and where the eccentricity of the disturbing planet is identically equal to zero. This procedure may be extended to the case where the eccentricity of the disturbing planet is not identically equal to zero. The two quadratures expressing the angular, slow Delaunay canonical variable lambda-prime(1) of the disturbed planet and the slow Delaunay canonical variable lambda-prime(2) of the disturbing planet are calculated for the latter, general case in terms of time t.
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