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Fig. 2. Vertical acceleration of the COM during walking as derived via the LiMb model. During walking the COM follows a sinusoidal trajectory in the sagittal plane resulting in alternating periods of upward and downward acceleration (+a_y and –a_y) during which the COM is accelerated. Maximum velocity, ±V_max, is a function of the precise shape of the COM trajectory. Assuming that V_max=2V_avg during normal walking, the change in velocity (i.e., the mass-specific change in momentum) during one period of acceleration, V_y=4L[1–cos(/2)](U^–1[Lsin(/2)])^–1 and thus V_y=4U[1–cos(/2) sin(/2)]^–1. Given the duration of acceleration, U^–1[Lsin(/2)], this requires an average acceleration _y=4U[1–cos(/2)]sin(/2)^–1(U^–1[Lsin(/2)])^–1 and thus _y=4U²L^–1[1–cos(/2)]sin(/2)^–2. Because sin(/2)^–2=([1–cos(/2)][1+cos(/2)])^–1, this simplifies to _y=4U²L^–1[1+cos(/2)]^–1.

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