Programmed analytical theory on the physical libration of the moon

Details Programmed analytical theory on the physical libration of the moon Programmed analytical theory on the physical libration of the moon

Feb 1976

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976moon...15..165m&link_type=abstract

The Moon, vol. 15, Jan.-Feb. 1976, p. 165-181. In French.

Mathematics

2

Hamiltonian Functions, Libration, Lunar Rotation, Selenology, Canonical Forms, Earth Orbits, Iterative Solution, Series (Mathematics), Tables (Data)

Scientific paper

The rotation of the moon about its center of mass, taking into account the orbital motion, is treated analytically. A Hamiltonian theory is developed in terms of the Andover variables. The periodic parts of departures from three resonances, equivalent to Cassini's laws, are found to be the canonical variables of the problem. The potential is expressed as a function of these new coordinates, and the whole Hamiltonian is developed to the second degree in these small variables. One system of equations gives the real center of libration, which is found to be near the center defined by Cassini's laws. A second system, solved by iterations, gives the libration as analytical series in the constants of the moon's potential and also as trigonometric series in Delaunay arguments.

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