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

L. Gergely, Mitchell McKain

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

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
Volume17
Issue number9
DOIs
Publication statusPublished - May 7 2000

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three body problem
curvature
geometry
tensors
scalars
symmetry
configurations

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

The geometry of the Barbour-Bertotti theories : II. The three-body problem. / Gergely, L.; McKain, Mitchell.

In: Classical and Quantum Gravity, Vol. 17, No. 9, 07.05.2000, p. 1963-1978.

Research output: Contribution to journalArticle

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