  We introduce suitable coordinate systems for interacting many-body systems
with invariant manifolds. These are Cartesian in coordinate and momentum space
and chosen such that several components are identically zero for motion on the
invariant manifold. In this sense these coordinates are collective. We make a
connection to Zickendraht's collective coordinates and present certain
configurations of few-body systems where rotations and vibrations decouple from
single-particle motion. These configurations do not depend on details of the
interaction.
