Non integrability of the n body problem with non zero angular momentum

Abstract

We prove an integrability criterion and a partial integrability criterion for homogeneous potentials of degree -1 which are invariant by rotation. We then apply it to the proof of the meromorphic non-integrability of the n body problem with Newtonian interaction in the plane on a surface of equation $(H,C)=(H_0,C_0)$ with $(H_0,C_0)\ne (0,0)$ where C is the angular momentum and H the energy, in the case where the n masses are equal.

30 pages, 14 references

References in corpus (4)

• Central Configurations of the Five-Body Problem with Equal Masses
• Central configurations for the planar Newtonian Four-Body problem
• On some exceptional cases in the integrability of the three-body problem
• Straight Line Orbits in Hamiltonian Flows

Cited by in corpus (4)

• A note on algebraic potentials and Morales-Ramis theory
• Non-integrability of the dumbbell and point mass problem
• Non integrability of a self-gravitating Riemann liquid ellipsoid
• Non-integrability of the minimum-time Kepler problem