Astronomy and Astrophysics – Astronomy
Scientific paper
Oct 1976
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976azh....53.1110b&link_type=abstract
Astronomicheskii Zhurnal, vol. 53, Sept.-Oct. 1976, p. 1110-1118. In Russian.
Astronomy and Astrophysics
Astronomy
1
Celestial Mechanics, Existence Theorems, Gravitational Fields, Rotating Bodies, Translational Motion, Equations Of Motion, Libration, Mercury (Planet), Planetary Rotation, Rigid Structures, Two Body Problem
Scientific paper
The existence of periodic solutions for the problem of translational-rotational motions of a rigid body exhibiting a plane of dynamical symmetry in the field of attraction of a sphere is investigated, and the Poincare small-parameter method is brought to bear. A complete system of existence conditions is set up for the periodic solutions, which are studied qualitatively in the large and numerically. Periodic motions on orbits of finite eccentricity are shown to exist, depending on the dynamical structure of the rigid body and on the type of commensurability in the rotational and orbital motions of the body. The results are useful for arriving at predictions of physical libration parameters for the earth's moon and for the planet Mercury.
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