# The Margin of Stability During a Single-Turn Pirouette in Female Amateur Dancers: A Pilot Study
## 1 Introduction
These studies suggest that the IPM should be substituted by a double inverted pendulum, which can be characterized as a kind of optimal, biaxial active controller used to minimize the acceleration of the body's CoM. However, more recently, [PERSON] et al. [11] demonstrated that while the single IPM may be \"literally\" an inadequate model to characterize the complexity of postural control because it ignores the ankle-knee-hip interactions, it is functionally correct for experimental studies that focus on the postural oscillations of the CoM. The IPM model has only recently been applied to the study of ballet. [PERSON] [12] applied the model to investigate how the number of pirouette rotations affected dynamic balance. She found the IPM to be beneficial as a reference model; however, for the intermediate-advanced dancers in her study, she found that their BoS, i.e., CoP, shifted to maintain balance during their turns [12]. These findings differ from the traditional IPM, due to the dynamic nature of a pirouette. It is notable that the IPM does not account for the whole-body axial rotations that occur with a pirouette, and the righting strategies associated with the IPM are based on a fixed BoS, whereas the pirouette is a dynamic movement with dynamic righting strategies, with potential for an unstable BoS. When performing the pirouette, the BoS transitions from a double-leg stance to a single-leg stance, which greatly decreases the area within the BoS. Therefore, an en dehors  
Figure 2: Inverted pendulum model. The body’s total mass minus the foot mass (m) times gravity (g) is balanced on top of the lower extremity, whose length = l; u = the CoP location; effective ground reaction force = -mg; x = the projected CoM onto the ground; and the BoS is the plantar portion of the foot that is in contact with the ground [13]. The yz plane reflects the orientation of the laboratory coordinate system. priouette requires the body's CoM to shift toward the stance leg during the turn initiation phase to allow the body's CoM to remain centered over the stance leg during the turn phase [2]. Velocity is generated during the turn initiation phase to bring the dancer up onto their stance leg and to spin the body around for the desired number of revolutions. Generally, to maintain balance, the CoM must stay within the BoS, but there are other factors involved in maintaining dynamic balance. According to [PERSON] et al. [13], if the velocity of the CoM is directed outward then balance may be lost even if the individual is within the BoS, and if one's CoM is outside of the BoS but their velocity is directed inward then balance may be maintained. This effect of an individual's velocity of the CoM during a dynamic movement is expressed as the extrapolated center of mass (XCoM), which is the velocity-adjusted position of the CoM [14]. Applying this concept to investigate turns performed by ballet dancers makes intuitive sense. In generating enough angular velocity to perform the pirouette, a dancer must also be able to control the direction of their velocity to remain balanced during their turn. It has been shown that changes in the relative positions of the CoP and XCoM are useful tools in the examination of balance and its perturbation [14]. The distance between the XCoM and the dancer's BoS that still allows them to maintain their balance and successfully complete their pirouette has been defined as the margin of stability (MoS) [14]. The MoS is determined as a time series throughout the movement and is the deviation of the XCoM from the BoS; its magnitude provides a metric of the dancer's dynamic balance. The MoS is thought to be proportional to the impulse needed to unbalance a participant [13]. The MoS could be related to the amount of self-generated impulse or disruption of balance that a dancer experiences during the turn initiation or turn phase of their pirouette. Traditionally, the IPM has been applied to study quiet standing postures, i.e., a static BoS [4; 5].