Astronomy and Astrophysics – Astronomy
Scientific paper
Jan 2004
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004cemda..88...37w&link_type=abstract
Celestial Mechanics and Dynamical Astronomy, v. 88, Issue 1, p. 37-49 (2004).
Astronomy and Astrophysics
Astronomy
1
Scientific paper
We consider Hill's lunar problem as a perturbation of the integrable two-body problem. For this we avoid the usual normalization in which the angular velocity ω of the rotating frame of reference is put equal to unity and consider ω as the perturbation parameter. We first express the Hamiltonian H of Hill's lunar problem in the Delaunay variables. More precisely we deduce the expressions of H along the orbits of the two-body problem. Afterwards with the help of the conserved quantities of the planar two-body problem (energy, angular momentum and Laplace-Runge-Lenz vector) we prove that Hill's lunar problem does not possess a second integral of motion, independent of H, in the sense that there exist no analytic continuation of integrals, which are linear functions of ω in the rotating two-body problem. In connection with the proof of this main result we give a further restrictive statement to the nonintegrability of Hill's lunar problem.
Meletlidou Efi
Winterberg Fabian Josef
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