A control theoretic approach to the swimming of microscopic organisms

Martín, Jorge; Takahashi, Takéo; Tucsnak, Marius

doi:10.1090/S0033-569X-07-01045-9

Authors: Jorge San Martín, Takéo Takahashi and Marius Tucsnak
Journal: Quart. Appl. Math. 65 (2007), 405-424
MSC (2000): Primary 76D05
DOI: https://doi.org/10.1090/S0033-569X-07-01045-9
Published electronically: May 21, 2007
MathSciNet review: 2354880
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Abstract: In this paper, we give a control theoretic approach to the slow self-propelled motion of a rigid body in a viscous fluid. The control of the system is the relative velocity of the fluid with respect to the solid on the boundary of the rigid body (the thrust). Our main results show that there exists a large class of finite-dimensional input spaces for which the system is exactly controllable, i.e., one can find controls steering the rigid body into any final position with a prescribed velocity field. The equations we use are motivated by models of swimming of micro-organisms like cilia. We give a control theoretic interpretation of the swimming mechanism of these organisms, which takes place at very low Reynolds numbers.

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