Relational shape space

The relational shape space of a particle configuration is obtained by removing collective translations and rotations; here scale is retained. For generic collision-free, noncollinear configurations of $N\ge 3$ labelled particles in three dimensions, the resulting configuration dimension is $3N-6$. Collinear configurations have nontrivial rotational stabilizers and require singular strata. Removing position and orientation does not automatically remove conserved angular momentum or its centrifugal effect; a dynamically faithful reduction must retain the appropriate momentum-level data.