  The inspiral of a turbulent molecular cloud in the Galactic Centre may result
in the formation of a small, dense and moderately eccentric gas disc around the
supermassive black hole (SMBH). Such a disc is unstable to fragmentation and
may lead to the formation of young massive stars in the central parsec of the
Galaxy. Here we perform high-accuracy direct summation N-body simulations of a
ring of massive stars (with initial semi-major axes 0.1 < a/pc < 0.4 and
eccentricities 0.2 < e < 0.4), subject to the potential of the SMBH, a stellar
cusp, and the parent gas disc, to study how the orbital elements of the ring
evolve in time. The initial conditions for the stellar ring are drawn from the
results of previous simulations of molecular cloud infall and disruption in the
SMBH potential. While semi-major axes do not evolve significantly, the
distribution of eccentricities spreads out very fast (~1 Myr) as a consequence
of cusp precession. In particular, stellar orbits with initial eccentricity
e>0.3 (e<0.3) tend to become even more (less) eccentric, resulting in a bimodal
eccentricity distribution. The distribution is qualitatively consistent with
that of the massive stars observed in the Galactic Centre's clockwise disc.
