Fig. 1. Swimming motions and kinematic variables. (A) A swimming hagfish (TL 31.5 cm), as represented by overlaid, reconstructed midlines (31 points each) from one tailbeat cycle. (B) Midlines displaced vertically (time descends) to show curvature and forward progression (17.5 cm s^-1). Inset: Midlines at times 0.20 s and 0.27 s are magnified to show placement of points 0-30 evenly along the midline. (C) The curvature half-wave length, /2 (L), is the axial distance along the midline from the points of 0 to 0 midline curvature, (m^-1). (D) Other kinematic variables include amplitude of the midline curvature, ₀, amplitude of the lateral displacement of body points 11, _0,11, and 30, _0,30, amplitude of the pitch angle, ₀. The phase lags _y— and _y—, are the differences in time, as a fraction of the normalized tailbeat period (T), between maximal and maximal and , respectively.