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Figure 3


Fig. 3. The four phases of the bounce of the body. Same subjects and speeds as in Fig. 1. In (A–F) the trend of the EpEk transduction, Rint(t) (black), is illustrated with the simultaneous changes in gravitational potential energy, Ep, and kinetic energy, Ek=Ekv+Ekf (green), normalized to oscillate between zero and one. The colors in the Ep curve distinguish the fractions of the step where the vertical force exerted on the ground is greater than body weight (red), and lower than body weight (blue). The continuous Ep line indicates the contact phase whereas the dotted Ep line (light-blue) indicates the aerial phase (not present in A and B). The four phases correspond to the vertical displacement during the upward acceleration Sce,up (red) and deceleration Sae,up (blue), and the downward acceleration Sae,down (blue) and deceleration Sce,down (red). The vertical dotted lines are drawn through the two peaks of Ek and encompass the fraction of the step where the EpEk transduction occurs, as indicated by the increment of the Rint(t) curve. Note that, particularly in the old subject, the transduction of Ek into Ep during the lift (increment Rint,up of Rint(t), below crossing of the interrupted lines) is smaller than the transduction of Ep into Ek during the downward displacement (increment Rint,down of Rint(t), above crossing of the interrupted lines). This asymmetry is accompanied by a ballistic lift (almost nil in the old subject) smaller than the ballistic fall. In the horizontal tracts of the Rint(t) curve no transduction occurs between Ep and Ek and muscle-tendon units absorb Ep and Ek simultaneously (phase β), and increase Ep and Ek simultaneously (phase {alpha}). Whereas most of β is confined within Sce,down, {alpha} usually extends beyond Sce,up within a large fraction of Sae,up due to a continuing increase of Ek. Also this asymmetry is larger in the old subject. In summary, the following features of the landing–take-off asymmetry of the bounce of the body are shown: (i) a peak of Ek greater during the fall than during the lift, (ii) a transduction of Ep into Ek during the fall greater than the transduction of Ek into Ep during the lift (i.e. Rint,down>Rint,up), and (iii) a simultaneous decrement of Ek and Ep after landing shorter than the simultaneous increment of Ek and Ep before and after take-off (i.e. β<{alpha}). All these deviations from an elastic bounce are larger in the old subject.