  We can understand many recently-discovered features of flavor evolution in
dense, self-coupled supernova neutrino and antineutrino systems with a simple,
physical scheme consisting of two quasi-static solutions. One solution closely
resembles the conventional, adiabatic single neutrino
Mikheyev-Smirnov-Wolfenstein (MSW) mechanism, in that neutrinos and
antineutrinos remain in mass eigenstates as they evolve in flavor space. The
other solution is analogous to the regular precession of a gyroscopic pendulum
in flavor space, and has been discussed extensively in recent works. Results of
recent numerical studies are best explained with combinations of these
solutions in the following general scenario: (1) Near the neutrino sphere, the
MSW-like many-body solution obtains. (2) Depending on neutrino vacuum mixing
parameters, luminosities, energy spectra, and the matter density profile,
collective flavor transformation in the nutation mode develops and drives
neutrinos away from the MSW-like evolution and toward regular precession. (3)
Neutrino and antineutrino flavors roughly evolve according to the regular
precession solution until neutrino densities are low. In the late stage of the
precession solution, a stepwise swapping develops in the energy spectra of
$\nu_e$ and $\nu_\mu/\nu_\tau$. We also discuss some subtle points regards
adiabaticity in flavor transformation in dense neutrino systems.
