Total Collisions in the N-Body Shape Space

We discuss the total collision singularities of gravitational N-body problem on shape space. Shape space is relational configuration system obtained by quotienting ordinary with respect to similarity group translations, rotations, and scalings. For zero-energy gravitating system, dynamics can be constructed explicitly points collision, which are central zero momenta, analyzed in detail. It turns out that, even where scale not part description, equations motion diverge at (and only at) collision. construct study stratified total-collision manifold show space, singularity essential. There is, thus, no way evolve solutions through these points. This mirrors closely big bang general relativity, homogeneous-but-not-isotropic cosmological model Bianchi IX shows an essential bang. A simple modification general-relativistic (the addition a stiff matter field) changes into one whose shape-dynamical description allows for deterministic evolution singularity. suspect similarly, some would required order regularize model.