Mechanics of the Fouetté turn

The Fouetté turn in classical ballet is performed repeatedly on one leg with swinging of the free limbs, producing a continued sequence of turns with one turn leading into the next. The purpose of this study was to determine the possible time history profiles of the twisting torque between the supporting leg and the remainder of the body that will allow continued performances of the Fouetté turn. Simulations were performed using a model which comprised the supporting leg and the remainder of the body to find torque profiles that maintain the initial angular velocity so that the state after one revolution is the same as the initial state. The solution space of torque profiles was determined for various rotation times and coefficients of friction between foot and floor. As the time for one revolution became shorter the solution space became smaller and for a given turn time there was a lower limit on the coefficient of friction. As the frictional coefficient became smaller the solution space became smaller and for a given coefficient there was a lower limit on the turn time. Turns of a given tempo can be performed on floors with different friction by modifying the twisting torque profile. When a turn is completed with a net change in angular velocity this can be compensated for in the next turn by adjusting the twisting torque profile.