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-y00492nas a2200109   4500008004100000245010000041210006900141260001000210653001300220100002600233856012300259       2015                        en  d00aMathematical Models of Locomotion: Legged Crawling, Snake-like Motility, and Flagellar Swimming0 aMathematical Models of Locomotion Legged Crawling Snakelike Moti  bSISSA10aMotility1 aCicconofri, Giancarlo  uhttps://math.sissa.it/publication/mathematical-models-locomotion-legged-crawling-snake-motility-and-flagellar-swimming01569nas a2200181   4500008004100000022001400041245006000055210005800115300001400173490000700187520100500194653001901199653002201218653002801240100002601268700002201294856007101316       2015                        eng d  a0020-746200aMotility of a model bristle-bot: A theoretical analysis0 aMotility of a model bristlebot A theoretical analysis  a233 - 2390 v763 a<p>Bristle-bots are legged robots that can be easily made out of a toothbrush head and a small vibrating engine. Despite their simple appearance, the mechanism enabling them to propel themselves by exploiting friction with the substrate is far from trivial. Numerical experiments on a model bristle-bot have been able to reproduce such a mechanism revealing, in addition, the ability to switch direction of motion by varying the vibration frequency. This paper provides a detailed account of these phenomena through a fully analytical treatment of the model. The equations of motion are solved through an expansion in terms of a properly chosen small parameter. The convergence of the expansion is rigorously proven. In addition, the analysis delivers formulas for the average velocity of the robot and for the frequency at which the direction switch takes place. A quantitative description of the mechanism for the friction modulation underlying the motility of the bristle-bot is also provided.</p>10aBristle-robots10aCrawling motility10aFrictional interactions1 aCicconofri, Giancarlo1 aDeSimone, Antonio  uhttp://www.sciencedirect.com/science/article/pii/S0020746215000025