  Active dumbbell suspensions constitute one of the simplest model system for
collective swimming at low Reynolds number. Generalizing recent work, we derive
and analyze stroke-averaged equations of motion that capture the effective
hydrodynamic far-field interaction between two oscillating, asymmetric
dumbbells in three space dimensions. Time-averaged equations of motion, as
those presented in this paper, not only yield a considerable speed-up in
numerical simulations, they may also serve as a starting point when deriving
continuum equations for the macroscopic dynamics of multi-swimmer suspensions.
The specific model discussed here appears to be particularly useful in this
context, since it allows one to investigate how the collective macroscopic
behavior is affected by changes in the microscopic symmetry of individual
swimmers.
