  Oscillations of neutrino emerging from a supernova core are studied. In this
extremely high density region neutrino self interactions induce collective
flavor transitions. When collective transitions are decoupled from matter
oscillations, as for our chosen matter profile, an analytical interpretation of
the collective effects is possible, by means of a mechanical analogy with a
spherical pendulum. For inverted neutrino hierarchy the neutrino propagation
can be divided in three regimes: synchronization, bipolar oscillations, and
spectral split. Our simulation shows that averaging over neutrino trajectories
does not alter the nature of these three regimes.
