Low Reynolds number swimming: reciprocal strokes go nowhere
3-link Purcell
Net displacement: 0.00 | Cycle: 0 | Mode: Purcell
Purcell's 1977 lecture "Life at Low Reynolds Number": at Re → 0, the Navier-Stokes equation is linear and time-reversible.
A scallop with one hinge (1 DOF) opens and closes — but reversing time reverses motion exactly, giving zero net displacement.
The 3-link Purcell swimmer (2 hinges, 2 DOF) breaks time-reversal via phase lag between hinges, achieving net propulsion.
Net displacement per cycle ∝ amplitude² × sin(phase lag). Red trail = scallop (zero net), green = Purcell swimmer.