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

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

2007-12-13

arxiv.org/abs/0712.2047v1

2008 New J. Phys. 10 063016

Physics

Fluid Dynamics

24 pages, 12 figures

Scientific paper

10.1088/1367-2630/10/6/063016

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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