  The discovery of Pluto's small moons in the last decade brought attention to
the dynamics of the dwarf planet's satellites. With such systems in mind, we
study a planar $N$-body system in which all the bodies are point masses, except
for a single rigid body. We then present a reduced model consisting of a planar
$N$-body problem with the rigid body treated as a 1D continuum (i.e. the body
is treated as a rod with an arbitrary mass distribution). Such a model provides
a good approximation to highly asymmetric geometries, such as the recently
observed interstellar asteroid 'Oumuamua, but is also amenable to analysis. We
analytically demonstrate the existence of homoclinic chaos in the case where
one of the orbits is nearly circular by way of the Melnikov method, and give
numerical evidence for chaos when the orbits are more complicated. We show that
the extent of chaos in parameter space is strongly tied to the deviations from
a purely circular orbit. These results suggest that chaos is ubiquitous in
many-body problems when one or more of the rigid bodies exhibits non-spherical
and highly asymmetric geometries. The excitation of chaotic rotations does not
appear to require tidal dissipation, obliquity variation, or orbital resonance.
Such dynamics give a possible explanation for routes to chaotic dynamics
observed in $N$-body systems such as the Pluto system where some of the bodies
are highly non-spherical.
