Mathematics – Functional Analysis
Scientific paper
Apr 1979
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979azh....56..427l&link_type=abstract
Astronomicheskii Zhurnal, vol. 56, Mar.-Apr. 1979, p. 427-433. In Russian.
Mathematics
Functional Analysis
Celestial Mechanics, Many Body Problem, Symmetry, Trajectory Analysis, Coordinates, Equations Of Motion, Functional Analysis, Time Functions
Scientific paper
Conditions are studied for conservation of the symmetry properties of trajectories in the many-body problem in the case of a transition from an absolute to a moving system of coordinates. It is shown that symmetric trajectories with the same direction of motion are conserved in that coordinate system whose origin moves in the plane of motion of some of the bodies while one coordinate axis remains perpendicular to this plane. Symmetric trajectories with opposite directions of motion are found to be conserved in a coordinate system whose motion is characterized by time functions of the appropriate parity.
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