INTRODUCTION: This paper examines the conditions for equilibrium in 3 dimensions during a turn based on Euler's equations for rigid body dynamics. This advances the understanding of some of the positions skiers instinctively adapt to maintain line and balance in the absence of adequate fore-aft motion or torques. This understanding can assist in addressing root problems as opposed to reactions, or symptoms, in coaching. METHOD: There are several ways to satisfy Euler's equation for rigid body dynamics [1] in a ski turn: [...] [1] where the 1 axis points forward from the skier's center of mass, 2 is lateral and points to the skier's left and 3 is perpendicular to the slope pointing up. l is the skier's moment of inertia about a particular axis, and [...] is the skier's angular velocity about an axis, where [...]. Inward lean is required to maintain equilibrium with the centripetal force (mv2/r) and the slope modified gravity (g sin a) [2]: [...] [2] where a is the slope of the hill. RESULTS: If the skier changes the direction they are facing during a turn, i.e., stays square by rotating about the three axis, then two fore aft reactions are possible. Entering a turn requires either a forward rotation about the lateral axis, 2, with the upper body, or a torque about 2, in which is created by applying forward pressure. Exiting the turn requires the opposite, rearward rotation or pressure. Alternatively the skier can reduce the rotation about the upward axis, 3, by reversing, or counter rotating at the beginning of the turn and over rotating at the end of the turn so that they tend to face up the hill. If the time to turn is half a second, which might be near the minimum in slalom, then the magnitude of the torque is about 20 Nm for a 75 kg 176 cm skier. DISCUSSION: Skiers, who get into a reversed position, as shown in the third image in the photomontage in Fig. 1, could be doing so because they have been unable to provide a forward moment (M2) or acceleration [...]. In this case it appears due to loss of snow contact. The response, which is probably instinctive, is to reduce the rotation about a vertical axis [...] by a counter rotation of the shoulders and pulling the outside (right) foot back to make the second part of equation [1] small. At the end of the turn the opposite would be true. CONCLUSION: Euler's equations for rigid body dynamics can help to explain the need for movements observed in skiing.
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