Integral manifolds of the \(N\)-body problem
This paper is devoted to the study of level manifolds (for an ambient space of dimension greater than three) of angular momentum of a system of bodies and treats in a global way the question of reduction or elimination of the node. Two distinct phenomena are studied: critical points and critical points at infinity of the energy function restricted to the chosen level manifold of angular momentum; the critical points are relative equilibria of Lagrange type. In particular, in the 4-body problem the critical points at infinity produce at most 26 changes of topology. The last part of the paper gives a description of the integral manifold of the 3-body problem.
scientific article; zbMATH DE number 549635
scientific article