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Hamiltonian Theory of the Libration of the Moon

Published online by Cambridge University Press:  12 April 2016

Jacques Henrard  and
Michèle Moons
Jacques Henrard
Affiliation:
Department of Mathematics, Facultés Universitaires de Namur, B-5000 Namur, Belgium
Michèle Moons
Affiliation:
Department of Mathematics, Facultés Universitaires de Namur, B-5000 Namur, Belgium

Abstract

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The feasibility of applying the Lie transform method to the problem of the physical libration of the Moon is investigated. By a succession of canonical transformations, the Hamiltonian of the problem is brought under a form suitable for perturbation technique. The mean value of the inclination of the angular momentum upon the ecliptic and the frequencies of the free libration are computed.

Type
Part II. Lunar Theory and Minor Planet Motions
Information
International Astronomical Union Colloquium , Volume 41: Dynamics of Planets and Satellites and Theories of their Motion , 1978 , pp. 125 - 135
Copyright
Copyright © Reidel 1978

References

Deprit, A.: 1967, Free Rotation of a Rigid Body Studied in the Phase Plane, Amer. J. of Physics, 35, 424.Google Scholar
Deprit, A. and Henrard, J.: 1971a, Analytical Lunar Ephemeris: the Variational Orbit, Astron. J., 76, 273.Google Scholar
Deprit, A., Henrard, J. and Rom, A.: 1971b, Analytical Lunar Ephemeris: Delaunay’s Theory, Astron. J., 76, 269.Google Scholar
Cook, A.H.: 1976, Theories of Lunar Libration, in Methods and Applications of Ranging to Artificial Satellites and the Moon, (print).Google Scholar
Eckhardt, D.H.: 1965, Computer Solutions of the Forced Physical Librations of the Moon, Astron. J., 70, 466.CrossRefGoogle Scholar
Eckhardt, D.H.: 1973, The Moon, 6, 127 CrossRefGoogle Scholar
Henrard, J.: 1972, Analytical Lunar Ephemeris: a report, Publication du Département de Mathématique F.U.N., Namur, Belgium.Google Scholar
Henrard, J.: 1974, Virtual Singularities in the Artificial Satellite Theory, Celestial Mechanics, 10, 437.Google Scholar
Jeffreys, H.: 1961, On the Figure of the Moon, Monthly N. of the R.A.S., 122, 421.Google Scholar
Migus, A.: 1976, Théorie Analytique Programmée de la Libration Physique de la Lune, The Moon, 15, 165.Google Scholar