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

Galactic Spiral Arms: Structure and Dynamics Given by an Equation of Motion