  Many active matter systems, especially on the microscopic scale, are well
approximated as overdamped, meaning that any inertial momentum is immediately
dissipated by the environment. On the other hand, especially for macroscopic
active systems but also for many mesoscopic systems the time scale of inertial
motion can become large enough to be relevant for the dynamics. This raises the
question how collective dynamics and the resulting states in active matter are
influenced by inertia. Therefore, we propose a coarsegrained continuum model
for underdamped active matter based on a mean field description for passive
systems. Furthermore, we apply the model to a system with interactions that
support an alignment on short distances and an antialignment on longer length
scales as known in the context of pattern formation due to orientational
interactions. Our numerical calculations of the underand overdamped dynamics
both predict a structured laning state. However, activity induced convective
flows that are only present in the underdamped model destabilize this state
when the anti-alignment is weakened, leading to a collective motion state which
does not occur in the overdamped limit. A turbulent transition regime between
the two states can be characterized by strong density fluctuations and the
absence of global ordering.
