Hi Ton ,
Many thanks for joining the discussion and for adding a bit of mathematical elegance to proceedings .

However , things may be bit more complex than just the vertical acceleration of the pelvis (as discussed above ) causing angular acceleration of the swing leg .

Through the spinal column , such accelerations of the pelvis will , as you say , accelerate the whole body upwards and this in turn may produce an angular acceleration of the swinging arms , even though they are swinging in different directions at any given time .

Thus the vertical forces produced by the standing leg will feed energy into 3 pendulums and not just one .