NDLI: The rectilinear three-body problem

Content Provider	Springer Nature Link
Author	Orlov, Victor Vladimirovich Petrova, Anna V. Tanikawa, Kiyotaka Saito, Masaya M. Martyva, Alija I.
Copyright Year	2008
Abstract	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.
Starting Page	93
Ending Page	120
Page Count	28
File Format	PDF
ISSN	09232958
Journal	Celestial Mechanics and Dynamical Astronomy
Volume Number	100
Issue Number	2
e-ISSN	15729478
Language	English
Publisher	Springer Netherlands
Publisher Date	2008-01-09
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Three-body problem Rectilinear three-body problem Triple approaches Schubart periodic orbit Escapes Ejections Mathematics Astronomy
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Mathematical Physics Astronomy and Astrophysics Modeling and Simulation Computational Mathematics Space and Planetary Science

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