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

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 analyzed 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 $N\ne 3$, are investigated. None of the independent scalars formed from the metric and curvature tensor diverges there.

16 pages, 2 eps figures, to appear in Classical and Quantum Gravity

References in corpus (1)

• The geometry of the Barbour-Bertotti theories I. The reduction process

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