  The transformation from angle-action variables to Cartesian coordinates is a
crucial step of the (semi) classical description of bimolecular collisions and
photo-fragmentations. The basic reason is that dynamical conditions
corresponding to experiments are ideally generated in angle-action variables
whereas the classical equations of motion are ideally solved in Cartesian
coordinates by standard numerical approaches. To our knowledge, the previous
transformation is available in the literature only for triatomic systems. The
goal of the present work is to derive it for polyatomic ones.
