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arXiv · 0712.2047

A geometric theory of swimming: Purcell's swimmer and its symmetrized cousin

J. E. Avron·O. Raz
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Abstract

We develop a qualitative geometric approach to swimming at low Reynolds number which avoids solving differential equations and uses instead landscape figures of two notions of curvatures: The swimming curvature and the curvature derived from dissipation. This approach gives complete information for swimmers that swim on a line without rotations and gives the main qualitative features for general swimmers that can also rotate. We illustrate this approach for a symmetric version of Purcell's swimmer which we solve by elementary analytical means within slender body theory. We then apply the theory to derive the basic qualitative properties of Purcell's swimmer.

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BibTeXRIS

J. E. Avron, O. Raz. 2007-12-13. A geometric theory of swimming: Purcell's swimmer and its symmetrized cousin. https://doi.org/10.1088/1367-2630%2F10%2F6%2F063016

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