Mathematics – Complex Variables
Scientific paper
Jan 1978
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978cemec..17...49a&link_type=abstract
Celestial Mechanics, vol. 17, Jan. 1978, p. 49-81. In Russian.
Mathematics
Complex Variables
Astrodynamics, Celestial Mechanics, Three Body Problem, Trajectory Analysis, Classifications, Complex Variables, Gravitational Fields, Liouville Equations, Roots Of Equations
Scientific paper
A qualitative analysis and a classification of the types of motion possible in the generalized plane problem of three fixed centers are presented. The method of Alekseev (1965) is used to determine the types of motion of a passively gravitating material point (a satellite) that are possible in the Newtonian gravitational field of three fixed centers having real, negative, or complex masses. The types of motion possible in the material case, the complex case, and the interior version of the problem are evaluated. It is shown that no singularities appear in the second coordinates in those cases where there are regions, lines, and points corresponding to possible motions; as a result, the second coordinates impose no additional constraints on the determined regions of possible real motion.
Arazov G. T.
Gabibov S. A.
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