Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

A control theoretic approach to the swimming of microscopic organisms


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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Additional Information

Jorge San Martín
Affiliation: Departamento de Ingeniería Matemática, Universidad de Chile, Casilla 170/3 - Correo 3, Santiago, Chile
Email: jorge@dim.uchile.cl

Takéo Takahashi
Affiliation: Institut Élie Cartan UMR7502, Université Henri Poincaré Nancy 1, BP239, 54506 Vandœuvre-lès-Nancy Cedex, France
Email: takahash@iecn.u-nancy.fr

Marius Tucsnak
Affiliation: Institut Élie Cartan UMR7502, Université Henri Poincaré Nancy 1, BP239, 54506 Vandœuvre-lès-Nancy Cedex, France
Email: tucsnak@loria.fr

DOI: https://doi.org/10.1090/S0033-569X-07-01045-9
Received by editor(s): July 25, 2005
Published electronically: May 21, 2007
Article copyright: © Copyright 2007 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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