Astronomy and Astrophysics – Astronomy
Scientific paper
Feb 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008cemda.100...93o&link_type=abstract
Celestial Mechanics and Dynamical Astronomy, Volume 100, Issue 2, pp.93-120
Astronomy and Astrophysics
Astronomy
4
Three-Body Problem, Rectilinear Three-Body Problem, Triple Approaches, Schubart Periodic Orbit, Escapes, Ejections
Scientific paper
The rectilinear equal-mass and unequal-mass three-body problems are considered. The first part of the paper is a review that covers the following items: regularization of the equations of motion, integrable cases, triple collisions and their vicinities, escapes, periodic orbits and their stability, chaos and regularity of motions. The second part contains the results of our numerical simulations in this problem. A classification of orbits in correspondence with the following evolution scenarios is suggested: ejections, escapes, conditional escapes (long ejections), periodic orbits, quasi-stable long-lived systems in the vicinity of stable periodic orbits, and triple collisions. Homothetic solutions ending by triple collisions and their dependence on initial parameters are found. We study how the ejection length changes in response to the variation of the triple approach parameters. Regions of initial conditions are outlined in which escapes occur after a definite number of triple approaches or a definite time. In the vicinity of a stable Schubart periodic orbit, we reveal a region of initial parameters that corresponds to trajectories with finite motions. The regular and chaotic structure of the manifold of orbits is mostly defined by this periodic orbit. We have studied the phase space structure via Poincaré sections. Using these sections and symbolic dynamics, we study the fine structure of the region of initial conditions, in particular the chaotic scattering region.
Martynova Alija I.
Orlov Victor Vladimirovich
Petrova Anna V.
Saito Masaya M.
Tanikawa Kiyotaka
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