Astronomy and Astrophysics – Astronomy
Scientific paper
Apr 1977
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977sva....21..232b&link_type=abstract
(Astronomicheskii Zhurnal, vol. 54, Mar.-Apr. 1977, p. 413-424.) Soviet Astronomy, vol. 21, Mar.-Apr. 1977, p. 232-237. Transla
Astronomy and Astrophysics
Astronomy
1
Celestial Mechanics, Center Of Gravity, Equations Of Motion, Kepler Laws, Many Body Problem, Perturbation Theory, Canonical Forms, Fourier Series, Hamilton-Jacobi Equation, Laplace Equation, Rotating Bodies, Translational Motion
Scientific paper
The Hamilton-Jacobi method is used to derive differential equations of rotational-translational motion for an n-body planetary system in which one body is somewhat more massive than the others. Keplerian motion of the mass centers in the appropriate Jacobi coordinate system and free rotational motion of the bodies relative to their own mass centers are taken as unperturbed motion in the general case, the free rotational motion of a body with an axis of symmetry is selected as the unperturbed motion of nearly axisymmetric bodies, and free Eulerian motion is adopted as the unperturbed motion of a body of arbitrary dynamic structure. The equations of rotational-translation motion are obtained in Jacobi's and Delaunay's canonical osculating elements as well as in Delaunay's 'action-angle' variable elements; these equations admit four first integrals (an energy integral and three area integrals). The classical celestial-mechanics theorems of Laplace and Lagrange are generalized to the case of an n-body planetary system
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