Anguilliform body dynamics: a continuum model for the interaction between muscle activation and body curvature

A two dimensional continuum model for the body mechanics of the lamprey is derived from a simple discrete rod and pivot structure. Each element in the discrete structure consists of two smoothly jointed light rods with perpendicular extensions at each of the midpoints between which is fixed a quasi muscle segment. The muscle segment is attributed with the viscous and elastic properties of all the animal tissue plus the ability to produce force. The travelling wave of muscle activation in the real animal is modelled by a corresponding time dependent forcing term at each segment. A linearisation of the ensuing continuum model, corresponding to low curvature dynamics, is investigated. The profiles obtained compare favourably with those of a lamprey moving out of water on a smooth surface. In addition the phase difference at each point on the body between the wave of muscle activation and the mechanical wave observed on the body indicates that the mechanical wave progresses slower than, but at the same frequency as, the wave of activation; this is a property that is also observed in the freely swimming lamprey.