Fig. 3. Coordinate system used for elongated body theory calculations. The solid line represents a midline at one time, while the dotted line represents it at a later time. Perpendicular and parallel velocity, v_⊥ and v||, are shown as vectors at the point (x_b, y_b). The arc length s is shown along the midline and the eel is swimming into a flow U. L is total body length.