Global phase structure of the restricted isosceles threebody problem with positive energy
Authors:
Kenneth Meyer and Qiu Dong Wang
Journal:
Trans. Amer. Math. Soc. 338 (1993), 311336
MSC:
Primary 70F07; Secondary 58F40
MathSciNet review:
1136546
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Abstract: We study a restricted threebody problem with special symmetries: the restricted isosceles threebody problem. For positive energy the energy manifold is partially compactified by adding boundary manifolds corresponding to infinity and triple collision. We use a new set of coordinates which are a variation on the McGehee coordinates of celestial mechanics. These boundary manifolds are used to study the global phase structure of this gradational system. The orbits are classified by intersection number, that is the number of times the infinitesimal body cross the line of syzygy before escaping to infinity.
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 Lacomba and L. Losco, Triple collision in the isosceles threebody problem, Bull. Amer. Math. Soc. 3 (1980), 489492. MR 571374 (81h:70003)
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 , Orbits of the threebody problem which pass infinitely close to triple collision, Amer. J. Math. 103 (1981), 13231341. MR 636961 (83d:58028)
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 Marchel and D. Saari, On the final evolution of the body problem, J. Differential Equations 20 (1976), 150186. MR 0416150 (54:4226)
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 [C]
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 2.
 QD. Wang, Qualitative study of body problem: Unitized momentum transformation and its application, Space Dynamics and Celestial Mechanics (K. B. Bhatnagar, ed.), Reidel, 1986, pp. 6169.
 3.
 , The global solution of body problem, Celestial Mech. 50 (1991), 7381.
 4.
 ZH. Xia, The existence of noncollision singularity in Newtonian gravitational system, preprint.
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DOI:
http://dx.doi.org/10.1090/S00029947199311365461
PII:
S 00029947(1993)11365461
Article copyright:
© Copyright 1993
American Mathematical Society
