Controllability properties of a class of systems modeling swimming microscopic organisms

Details Controllability properties of a class of systems modeling swimming microscopic organisms Controllability properties of a class of systems modeling swimming microscopic organisms

2007-11-15

arxiv.org/abs/0711.2488v2

Mathematics

Optimization and Control

Scientific paper

We consider a finite-dimensional model for the motion of microscopic organisms whose propulsion exploits the action of a layer of cilia covering its surface. The model couples Newton's laws driving the organism, considered as a rigid body, with Stokes equations governing the surrounding fluid. The action of the cilia is described by a set of controlled velocity fields on the surface of the organism. The first contribution of the paper is the proof that such a system is generically controllable when the space of controlled velocity fields is at least three-dimensional. We also provide a complete characterization of controllable systems in the case in which the organism has a spherical shape. Finally, we offer a complete picture of controllable and non-controllable systems under the additional hypothesis that the organism and the fluid have densities of the same order of magnitude.

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