 |
|
|
|
| HAL : hal-00140543, version 1 |
| Fiche détaillée |  Récupérer au format |
|
|
| Quarterly of Applied Mathematics 65, 3 (2007) 405--424 |
|
|
|
|
| A Control Theoretic Approach to the Swimming of Microscopic Organisms |
|
|
| Jorge San Martin 1Takéo Takahashi 2, 3 |
|
|
| (2007) |
|
|
|
| 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 in 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. Our aim is to give a control theoretic interpretation of the swimming mechanism of micro-organisms (like ciliata) which is one of the fascinating problems in fluid mechanics. |
|
|
|
|
|
|
|
|
|
|
|
| 1 : | Centre de Modélisation Mathématique / Centro de Modelamiento Matemático (CMM) |
|
|
|
CNRS : UMR2071 |
|
|
| 2 : | CORIDA (INRIA Nancy - Grand Est / IECN / LMAM) |
|
|
|
INRIA – CNRS : UMR7502 – Université de Lorraine |
|
|
| 3 : | Institut Elie Cartan Nancy (IECN) |
|
|
|
CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL) |
|
|
|
|
|
|
|
|
|
| Domaine | : | Mathématiques/Optimisation et contrôle |
| hal-00140543, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00140543 | |
| oai:hal.archives-ouvertes.fr:hal-00140543 | |
| Contributeur : Marius Tucsnak | |
| Soumis le : Vendredi 6 Avril 2007, 17:18:50 | |
| Dernière modification le : Vendredi 26 Septembre 2008, 13:56:57 | |
