= 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 $N\ge3$ 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.
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