  (Abridged) We explore numerically the chemical, thermal, and dynamical
evolution of a shell formed by a high-energy supernova explosion ($10^{53}$
erg) in dwarf protogalaxies with total mass $10^7 M_\odot$ at a redshift
$z=12$. We consider two initial configurations for the baryonic matter, one
without rotation and the other having the ratio of rotational to gravitational
energy $\beta=0.17$. The (non-rotating) dark matter halo is described by a
quasi-isothermal sphere. We find that the dynamics of the shell is different in
protogalaxies with and without rotation. For instance, the Rayleigh-Taylor
instability in the shell develops faster in protogalaxies without rotation. The
fraction of a blown-away baryonic mass is approximately twice as large in
models with rotation ($\sim 20%$) than in models without rotation. On the other
hand, the chemical evolution of gas in protogalaxies with and without rotation
is found to be similar. The relative number densities of molecular hydrogen and
HD molecules in the cold gas ($T \le 10^3$ K) saturate at typical values of
$10^{-3}$ and $10^{-7}$, respectively. The clumps formed in the fragmented
shell move with velocities that are at least twice as large as the escape
velocity. The mass of the clumps is $\sim 0.1-10 \msun$, which is lower than
the Jeans mass. We conclude that the clumps are pressure supported. A supernova
explosion with energy $10^{53}$ ergs destructs our model protogalaxy. The
clumps formed in the fragmented shell are pressure supported. We conclude that
protogalaxies with total mass $\sim 10^{7} M_\odot$ are unlikely to form stars
due to high-energy supernova explosions of the first stars.
