  Collective modes of interacting many-body systems can be related to the
motion on classically invariant manifolds. We introduce suitable coordinate
systems. These coordinates are Cartesian in position and momentum space. They
are collective since several components vanish for motion on the invariant
manifold. We make a connection to Zickendraht's collective coordinates and also
obtain shear modes. The importance of collective configurations depends on the
stability of the manifold. We present an example of quantum collective motion
on the manifold
