  A classical microscopic theory of rovibrational motion at high angular
momenta in symmetrical non-linear molecules AB$_2$ is derived within the
framework of small oscillations near the stationary states of a rotating
molecule. The full-dimensional analysis including stretching vibrations has
confirmed the existence of the bifurcation predicted previously by means of the
rigid-bender model. The formation of fourfold energy clusters has already been
experimentally verified for H$_2$Se and it has been demonstrated in
fully-dimensional quantum mechanical calculations using the MORBID computer
program. We show in the present work that apart from the level clustering, the
bifurcation produces physically important effects including molecular
symmetry-breaking and a transition from the normal mode to the local mode limit
for the stretching vibrations due to rovibrational interaction. The application
of the present theory with realistic molecular potentials to the H$_2$Te,
H$_2$Se and H$_2$S hydrides results in predictions of the bifurcation points
very close to those calculated previously. However for the lighter H$_2$O
molecule we find that the bifurcation occurs at higher values of the total
angular momentum than obtained in previous estimations. The present work shows
it to be very unlikely that the bifurcation in H$_2$O will lead to clustering
of energy levels. This result is in agreement with recent variational
calculations.
