  The dwarf galaxy distribution surrounding M31 is significantly anisotropic in
nature. Of the 30 dwarf galaxies in this distribution, 15 form a disc-like
structure and 23 are contained within the hemisphere facing the Milky Way.
Using a realistic local potential, we analyse the conditions required to
produce and maintain these asymmetries. We find that some dwarf galaxies are
required to have highly eccentric orbits in order to preserve the presence of
the hemispherical asymmetry with an appropriately large radial dispersion.
Under the assumption that the dwarf galaxies originate from a single
association or accretion event, we find that the initial size and specific
energy of that association must both be relatively large in order to produce
the observed hemispherical asymmetry. However if the association was large in
physical size, the very high-energy required would enable several dwarf
galaxies to escape from the M31 and be captured by the Milky Way. Furthermore,
we find that associations that result in this structure have total specific
energies concentrated around $E = V_{esc}^{2} - V_{init}^{2} \sim 200^2$ --
$300^2\ \rm{km^2\ s^{-2}}$, implying that the initial velocity and initial
position needed to produce the structure are strongly correlated. The overlap
of initial conditions required to produce the radial dispersion, angular
dispersion, and the planar structure is small and suggests that either they did
not originate from a single accretion event, or that these asymmetric
structures are short-lived.
