Every skier who enjoys skiing probably wishes to master parallel turns(Christies)repeated rhythmically in a stable manner. To repeat parallel turns, the skier needs to transpose his weight from one side edge of ski to another when he starts next turning. Furthermore, at that instant, the value of edging angle of ski passes through zero .Therefore, in the course of repeated parallel turns, the skier must perform smooth turning between unstable states of zero edging angle. In the present investigation, we assume a stick-pictured model of skier of which the rigid upper body is combined with the rigid lower body at the hip joints. The skier is assumed to be equipped with a single rigid ski in which an effective side-curve is formed. We take into account only one degree of freedom of skier's internal motion, namely, the rotation of hip joints (the rotation of upper body around the femur axes), which simulates the mechanism of the Alpine ski-robot. We derive the equations of motion and solve them numerically. The skier starts turning by carving turn along the effective side-curve of ski and then the skidding of ski takes place by the centrifugal force. When the value of edging angle of ski decreases down to zero, the weight of skier is transposed to the another edge of ski and the next turning begins towards counter side. We obtained the results corresponding to repeated parallel turns with long as well as short rhythm. These results show essential features of repeated parallel turns performed by a human skier and suggest how to practice skillful parallel turns.
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