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

2000/03/16 by L. Gergely, László Á Gergely, Mitchell McKain · 1 citation
Engineering · Physics and Astronomy · #Astro and Planetary Science #Planetary Science and Exploration #Spacecraft Dynamics and Control #gr-qc

paper · pdf · doi:10.1088/0264-9381/17/9/307

published as Class.Quant.Grav. 17 (2000) 1963-1978 · 16 pages, 2 eps figures, to appear in Classical and Quantum Gravity

arxiv created 2000/03/16 · openalex publication_date 2000/04/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

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.

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