Central configurations and hyperbolic-elliptic motion in the three-body problem

Details Central configurations and hyperbolic-elliptic motion in the three-body problem Central configurations and hyperbolic-elliptic motion in the three-body problem

Jan 1980

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980cemec..21...37h&link_type=abstract

(Conference on Mathematical Methods in Celestial Mechanics, 6th, Oberwolfach, West Germany, Aug. 14-19, 1978.) Celestial Mechani

Mathematics

2

Celestial Mechanics, Elliptical Orbits, Hyperbolic Trajectories, Three Body Problem, Boundary Value Problems, Equations Of Motion, Kinetic Energy, Spatial Distribution

Scientific paper

A refined classification of motion for the planar three-body problem with zero-sum total energy is presented. The structure and dimensions of the sets of initial conditions leading to parabolic expansion or hyperbolic-elliptic motion are found. Attention is given to the use of the Hamiltonian of the system and to the two- and three-dimensional problem. It is verified that the new coordinates of position and linear momentum approaches limits as t (time) approaches infinity, and that these limits constitute equilibrium solutions to the three-body problem representing control configurations.

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