The geometry of the Barbour-Bertotti theories: II. The three-body problem

László Á Gergely, Mitchell McKain

Research output: Contribution to journalArticle

20 Citations (Scopus)


We present a geometric approach to the three-body problem in the non-relativistic context of the Barbour-Bertotti theories. The Riemannian metric characterizing the dynamics is analysed in detail in terms of the relative separations. Consequences of a conformal symmetry are exploited and the sectional curvatures of geometrically preferred surfaces are computed. The geodesic motions are integrated. Line configurations, which lead to curvature singularities for N ≠ 3, are investigated. None of the independent scalars formed from the metric and curvature tensor diverges there.

Original languageEnglish
Pages (from-to)1963-1978
Number of pages16
JournalClassical and Quantum Gravity
Issue number9
Publication statusPublished - May 7 2000

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

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