Geometric characterization for variational minimization solutions of the 3-body problem with fixed energy

Authors
Long, YM Zhang, SQ
Citation
Ym. Long et Sq. Zhang, Geometric characterization for variational minimization solutions of the 3-body problem with fixed energy, J DIFF EQUA, 160(2), 2000, pp. 422-438
Citations number
26
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF DIFFERENTIAL EQUATIONS
ISSN journal
00220396 → ACNP
Volume
160
Issue
2
Year of publication
2000
Pages
422 - 438
Database
ISI
SICI code
0022-0396(20000120)160:2<422:GCFVMS>2.0.ZU;2-7
Abstract
In this paper, for any given positive masses we prove that the constrained variational minimization solutions of the fixed energy or fixed mean potent ial energy problem for the 3-body type problems with homogeneous potentials in R-3 or R-2 are precisely the planar equilateral triangle circular solut ions found by J. Lagrange in 1772.. (C) 2000 Academic Press.