  Using an equation of motion for a self-gravitating filament, we show how
galactic spiral arms might be created and sustained. We find that the
combination of differential rotation of the galactic disk and the self-gravity
of the arm (as given by the equation) leads to a rotating spiral structure.
Moreover, using this analysis, we then find a second differential equation that
explicitly relates this spiral structure to the rotation curve of the galaxy --
it connects several factors, including spiral shape and pattern speed. We also
describe a simple many-body numerical experiment that supports our approach.
The findings are with consistent with observational evidence concerning arm
structure and rotation curves, including leading arm structures.
