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Applied Math Colloquium

Friday, March 7th, 2014, 11:30 AM
Cullimore Lecture Hall, Lecture Hall II
New Jersey Institute of Technology

Optimizing snake locomotion in the plane

Silas Alben

University of Michigan, Ann Arbor

Abstract

Snake locomotion has recently drawn interest from biologists, engineers and applied mathematicians. Snakes propel themselves by a variety of gaits including slithering, sidewinding, concertina motion and rectilinear progression. We develop a numerical scheme to determine which planar snake motions are optimal for locomotory efficiency, across a wide range of frictional parameter space. For a large coefficient of transverse friction, we show that retrograde traveling waves are optimal. We give an asymptotic analysis showing that the optimal wave amplitude decays as the -1/4 power of the coefficient of transverse friction. This result agrees well with the numerical optima. At the other extreme, zero coefficient of transverse friction, we propose a triangular direct wave which is optimal. Between these two extremes, a variety of complex, locally optimal, motions are found. Some of these can be classified as standing waves (or ratcheting motions).