Symmetry of solutions in the N-body problem

Details Symmetry of solutions in the N-body problem Symmetry of solutions in the N-body problem

Dec 1978

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978azh....55.1293l&link_type=abstract

Astronomicheskii Zhurnal, vol. 55, Nov.-Dec. 1978, p. 1293-1300. In Russian.

Astronomy and Astrophysics

Astronomy

Astronomy, Equations Of Motion, Many Body Problem, Symmetry, Trajectory Analysis, Three Body Problem, Time Functions

Scientific paper

The possible existence of symmetric solutions to the equations of motion of the N-body problem in an absolute coordinate system is investigated. It is noted that such solutions are known to exist in the restricted three-body problem. Proof is given that symmetric solutions in the N-body problem can exist only if the trajectories of some of the bodies are planar or symmetrical with respect to a plane, line, or point with symmetric laws of motion. Reasons for the existence of the well-known symmetric solutions in the restricted three-body problem are determined.

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