The non-existence of centre-of-mass and linear-momentum integrals in the curved N-body problem
arXiv:1202.4739
Abstract
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.
arXiv comment12 pages