Classical Grand Angular Momentum in N-Body Problems

The concept of grand angular momentum is widely used in the study of N-body problems quantum mechanically. Here, we applied it to a classical analysis of N-body problems. Utilizing the tree representation for Jacobi and hyperspherical coordinates, we found a decomposition of its magnitude into magnitudes of regular angular momenta in 3 dimensions. We generalized some results from the two-body problem and derived a general expression for the scattering angle in the N-body case.