The effective pendulum length along the body's vertical axis (i.e., radius of gyration of the dancer's body around the topple axis) is determined from I = M[l.sub.eff.sup.2] (where M = body mass and I is the principal moment of inertia around the topple axis).
Caption: Figure 1 Inverted pendulum model with body mass concentrated at the CoM and the point of support and topple axis of rotation (perpendicular to the page) at the CoP.
The dancer with the mass concentrated lower in the hips will topple more easily because the mass is distributed closer to the topple axis of rotation at the floor.
The criterion for stability of a "sleeping" top (or dancer) is given by Equation 5, where [I.sub.z] is the moment of inertia of the dancer around the spin axis, s is the spin rate of the dancer's pirouette, m is the dancer's mass, g is the acceleration due to gravity (9.81 m/[s.sup.2]), l is the distance from the pivot point to the center of mass, and I is the moment of inertia of the dancer around the topple axis.
Instead, the equation of motion of a dancer toppling from a pirouette position is simply (from [SIGMA][tau] = I[alpha]), as show in Equation 6, where a is the dancer's angular acceleration around the topple axis.