Abstract
We examine the problem of snake-like locomotion by studying a model system consisting of a planar inextensible elastic rod that is able to control its spontaneous curvature. Using Cosserat theory we derive the equations of motion for two special cases: one in which the system is confined inside a channel with frictionless walls, and one in which the system is placed on an anisotropic frictional environment with an infinite contrast between longitudinal and transversal friction, so that the rod can slide longitudinally along its axis, but cannot slip laterally (i.e., in the transversal direction). The results obtained by solving these equations of motion are reminiscent of classical experimental results in the biological literature, and provide a scheme to rationalise the observed behaviour.
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