2000/03/16 by L. Gergely, László Á Gergely · 1 citation
Physics and Astronomy · #Astro and Planetary Science #Classical mechanics #Context (archaeology) #Cosmology and Gravitation Theories #Curvature #Degenerate energy levels #Differential geometry #Geometry #Mathematical analysis #Mathematical physics #Physics #Quantum mechanics #Relativity and Gravitational Theory #Riemann curvature tensor #Scalar (mathematics) #Scalar curvature #Tensor (intrinsic definition) #gr-qc
paper · pdf · doi:10.1088/0264-9381/17/9/306
published as Class.Quant.Grav.17:1949-1962,2000 · 15 pages, to appear in Classical and Quantum Gravity
arxiv created 2000/03/16 · openalex publication_date 2000/04/10 · arxiv updated 2014/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The dynamics of N 3 interacting particles is investigated in the non-relativistic context of the Barbour-Bertotti theories. The reduction process on this constrained system yields a Lagrangian in the form of a Riemannian line element. The involved metric, degenerate in the flat configuration space, is the first fundamental form of the space of orbits of translations and rotations (the Leibniz group). The Riemann tensor and the scalar curvature are computed using a generalized Gauss formula in terms of the vorticity tensors of generators of the rotations. The curvature scalar is further given in terms of the principal moments of inertia of the system. Line configurations are singular for N 3. A comparison with similar methods in molecular dynamics is traced.