01596nas a2200133   4500008004100000245010900041210006900150260001000219520113200229100002101361700002201382700002201404856003601426       2013                        en  d00aOne-dimensional swimmers in viscous fluids: dynamics, controllability, and existence of optimal controls0 aOnedimensional swimmers in viscous fluids dynamics controllabili  bSISSA3 a<p>In this paper we study a mathematical model of one-dimensional swimmers performing a planar motion while fully immersed in a viscous fluid. The swimmers are assumed to be of small size, and all inertial effects are neglected. Hydrodynamic interactions are treated in a simplified way, using the local drag approximation of resistive force theory. We prove existence and uniqueness of the solution of the equations of motion driven by shape changes of the swimmer. Moreover, we prove a controllability result showing that given any pair of initial and final states, there exists a history of shape changes such that the resulting motion takes the swimmer from the initial to the final state. We give a constructive proof, based on the composition of elementary maneuvers (straightening and its inverse, rotation, translation), each of which represents the solution of an interesting motion planning problem. Finally, we prove the existence of solutions for the optimal control problem of finding, among the histories of shape changes taking the swimmer from an initial to a final state, the one of minimal energetic cost.</p>1 aDal Maso, Gianni1 aDeSimone, Antonio1 aMorandotti, Marco  uhttp://hdl.handle.net/1963/6467