# The Margin of Stability During a Single-Turn Pirouette in Female Amateur Dancers: A Pilot Study
## 1 Introduction  
The pirouette is a fundamental movement in classical ballet. In this turn, the dancer balances on a single limb while on the toes (pointe) or on the ball of the foot (demi-pointe) and performs one or more whole-body revolutions around a pivot axis through the stance leg [1]. A pirouette is classified by the direction in which the turn is initiated. The direction most often seen in classical ballet choreography and research is the en dehors pirouette. This means that the dancer rotates outward, away from the stance leg. A pirouette can also be performed in en dedans by rotating inwards, toward the stance leg. In either turn, the leg used in push-off is lifted from the ground and held in a retire position (Figure 1). A pirouette consists of two phases: a turn initiation phase and a turn phase (Figure 1). The turn initiation phase begins with the dancer assuming a static double-leg stance in either the fourth or fifth position [1; 2]. In the fourth position, one foot rests about 12 inches in advance of the other, both are turned out, and the weight is divided between them, whereas in the fifth position, the feet are turned out and pressed closely together, with the heel of the one foot against the toe of the other. The turn phase is performed in a single-leg stance while the dancer completes one or more rotations at the pivot point through the stance leg, usually on the metatarsal heads [2]. During this phase, the turn leg works in an open kinematic chain, while the stance leg works in a closed kinematic chain and helps to control posture [3]. The inverted pendulum model (IPM) has been used to analyze the lower extremities' responses to internal and external perturbations to the body's center of mass (CoM). The IPM is based on the following assumptions: (1) simplification of the body's complex mass distribution by distributing it as a single point, i.e., the CoM, located at a fixed distance from the ankle pivot; (2) the legs are considered massless, perfectly rigid, and act as straight lines connecting the CoM to the ankle joint center; (3) the ankle axis is a fixed point, about which the leg rotates; (4) movement occurs in two planes, i.e., sagittal and frontal; and (5) there is no account of the effects of muscles and net joint moments at the knee and hip [4; 5]. Related to the IPM, lower extremity muscles are recruited to shift the center of pressure (CoP), which helps to maintain the CoM within the BoS [4]. The CoM is controlled in the sagittal plane by the ankle's dorsi-/plantar flexor muscles and in the frontal plane by the hip abductor/adductor and ankle invertor/evertor muscles, leading to a change in the CoP as a reaction to these adjustments; that is, changes in the position of the CoP are the central nervous system's response to perturbations [4]. [PERSON] et al. and [PERSON] et al. demonstrated that the difference between the locations of the CoM and the CoP, when projected on the ground (Figure 2), is positively related to the horizontal acceleration of the body's CoM [4; 5]. Therefore, as the horizontal acceleration of the CoM increases during a task, the distance between the CoP and CoM decreases, and vice versa. Figure 1: Two major phases of a pirouette. Prior to turn initiation (green box), the dancer assumes the 4 th position (far left). Turn initiation includes the toe-off (blue box) that segues in to the turn phase (red box). The turn is completed with a toe-touch event (2 nd blue box). Although the IPM has been validated for examining quiet standing [4; 5; 6] and gait [7], others have challenged the primary assumptions of the single inverted pendulum for the examination of quiet stance [8; 9] and gait [10]. In essence, with regard to postural control, these researchers have suggested that knee [9] and hip [8; 9; 10] motion during quiet stance cannot be neglected, and that ankle-hip oscillatory patterns are characterized by complex in-phase and anti-phase interactions.