Asymmetry and stability of shape kinematics in microswimmers' motion.

Many swimming microorganisms governed by low Reynolds number hydrodynamics utilize flagellar undulations for self-propulsion. Most of the existing theoretical models assume that the shape kinematics is directly controlled, while in reality, eukaryotes actuate internal bending moments along their flagellum. Under this control, the shape is dynamically evolving and periodic gaits may become unstable. This Letter addresses the problem by revisiting Purcell's three-link swimmer model where joint torques are controlled, and the geometric symmetries underlying the dynamics of the swimmer are analyzed. It is found that one has to break the front-back symmetry of the swimmer's structure and/or actuation profile in order to induce stable shape kinematics. The results may explain why most of the flagellated eukaryotes swim with their head forward.