01781nas a2200157   4500008004100000022001400041245006600055210006600121260000800187300000700195490000700202520131900209100002601528700002201554856004701576       2016                        eng d  a1292-895X00aMotion planning and motility maps for flagellar microswimmers0 aMotion planning and motility maps for flagellar microswimmers  cJul  a720 v393 a<p>We study two microswimmers consisting of a spherical rigid head and a passive elastic tail. In the first one the tail is clamped to the head, and the system oscillates under the action of an external torque. In the second one, head and tail are connected by a joint allowing the angle between them to vary periodically, as a result of an oscillating internal torque. Previous studies on these models were restricted to sinusoidal actuations, showing that the swimmers can propel while moving on average along a straight line, in the direction given by the symmetry axis around which beating takes place. We extend these results to motions produced by generic (non-sinusoidal) periodic actuations within the regime of small compliance of the tail. We find that modulation in the velocity of actuation can provide a mechanism to select different directions of motion. With velocity-modulated inputs, the externally actuated swimmer can translate laterally with respect to the symmetry axis of beating, while the internally actuated one is able to move along curved trajectories. The governing equations are analysed with an asymptotic perturbation scheme, providing explicit formulas, whose results are expressed through motility maps. Asymptotic approximations are further validated by numerical simulations.</p>1 aCicconofri, Giancarlo1 aDeSimone, Antonio  uhttps://doi.org/10.1140/epje/i2016-16072-y