On the elimination of the critical term in a general first-order Uranus-Neptune theory

Details On the elimination of the critical term in a general first-order Uranus-Neptune theory On the elimination of the critical term in a general first-order Uranus-Neptune theory

May 1981

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981m%26p....24..261k&link_type=abstract

Moon and the Planets, vol. 24, May 1981, p. 261-279.

Physics

2

Canonical Forms, Equations Of Motion, Neptune (Planet), Orbit Perturbation, Solar Orbits, Uranus (Planet), Von Zeipel Method, Eccentricity, Hamiltonian Functions, Poincare Problem

Scientific paper

A solution of the Uranus-Neptune planetary canonical equations of motion through the Von Zeipel technique is presented. A unique determining function which depends upon mixed canonical variables, reduces the 1:2 critical terms of the Hamiltonian to the set of its secular terms. The Poincare canonical variables are used. We refer to a common fixed plane, and apply the Jacobi-Radau set of origins. In our expansion we neglected terms of power higher than the fourth with respect to the eccentricities and sines of the inclinations.

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