Resonant and secular phenomena in the libration of the Moon

Details Resonant and secular phenomena in the libration of the Moon Resonant and secular phenomena in the libration of the Moon

Oct 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993cemda..57..404b&link_type=abstract

Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 57, no. 1-2, p. 404

Astronomy and Astrophysics

Astronomy

Astronomical Models, Earth Orbits, Libration, Long Term Effects, Lunar Rotation, Orbit Calculation, Orbit Perturbation, Orbital Resonances (Celestial Mechanics), Hamiltonian Functions, Mathematical Models, Solar Orbits

Scientific paper

Principal and subtle regularities, resonant and secular phenomena in the rotational motion of the Moon are investigated on the basis of the analytical solution of a model problem, in which the Moon and the Earth are considered as absolute rigid nonspherical bodies, and the Sun and the other planets are treated as material points. The orbital motion of all these bodies are considered as known and described by analytical theories. An analytical solution of the problem has been built on the basis of the canonical equations of the rotational motion of the Moon in the Andoyer's variables using the method of constructing conditionlly-periodic solutions of an Hamiltonian system depending upon a small parameter, and researching general solutions in their neighbourhood. The solution so constructed is used for analyzing the principal and subtle regularities, resonance phenomena in the rotational motion of the Moon, i.e. for studying the principal departure from the Cassini's laws in the rotational motion of the Moon due to the long periodic orbital perturbations of Moon and Sun.

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