Invariant manifolds and collective coordinates

We introduce suitable coordinate systems for interacting many-body systems with invariant manifolds. These are Cartesian in coordinate and momentum sp ace 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 c ertain configurations of few-body systems where rotations and vibrations de couple from single-particle motion. These configurations do not depend on d etails of the interaction.