Fig. 1.

Schematic showing the notation used in a moving frame of reference: A thin sheet of thickness $\mathit{\xi }$ and length L moves with velocity U in the negative x direction, through undulatory motions characterized by tail beat amplitude $A_{\lambda }$ (in dimensionless notation $\lambda =A_{\lambda }/L$). Unit vectors are denoted by $\mathbf{i}$ and $\mathbf{j}$.