Investigating Total Collisions of the Newtonian N-Body Problem on Shape Space

We analyze the points of total collision Newtonian gravitational system on shape space (the relational configuration system). While equations motion, formulated with respect to absolute and time, are singular at point due singularity Newton potential that point, this need not be case where scale doesn't exist. investigate whether, adopting a description system, degrees freedom, which merely angles their conjugate momenta, can evolved through collision. Unfortunately, is case. Even without scale, motion (and only there). This follows from special behavior momenta. induces singularity, it same time provides purely shape-dynamical collisions. By help this, we able discern total-collision solutions non-collision space, is, reference (external) scale. further use show form set measure zero among all solutions.