The non-existence of centre-of-mass and linear-momentum integrals in the curved N-body problem
classification
🧮 math.DS
math-phmath.MP
keywords
centre-of-masscurvedintegralslinear-momentumn-bodyproblemalongcentre
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We provide a class of orbits in the curved N-body problem for which no point that could play the role of the centre of mass is fixed or moves uniformly along a geodesic. This proves that the equations of motion lack centre-of-mass and linear-momentum integrals.
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